MATHSBOOKS - RS AGGARWAL MATHS

(HINGLISH)

VOLUME AND SURFACE AREA OFSOLIDS

Exercise 15 A

1. Find the volume, the lateral surface area and the total

surface area of the cuboid whose dimensions are:

(i) length = 12 cm, breadth = 8 cm and height = 4.5 cm

(ii) length = 26 m, breadth = 14 m and height = 6.5 m

(iii) length = 15m, breadth = 6 m and height = 5 dm

(iv) length = 24m, breadth = 25 cm and height = 6 m

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2. A matchbox measures

. What will be the

volume of a packet containing such boxes.

A.

B.

C.

D.

Answer: C

W t h Vid S l ti

4 cm  ×  2. 5 cm  ×  1. 5 cm

12

140cm3

120cm3

180cm3

160cm3

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3. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m

deep. How many litres of watercan it hold? (

)

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1 m3 =  1000l

4. The capacity of a cuboidal tank is 50000 litres of

water. Find the breadth of the tank, if its length and

depth are respectively 2.5 m and 10 m

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5. A godown measures .

Find the maximum number of wooden crates each

measuring that can be

stored in the godown.

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40 m  ×  25 m  ×  10 m

1. 5 m  ×  1. 25 m  ×  0. 5 m

6. How many planks of dimensions

can be stored in a pit which is

20m long, 6m wide and 80 cm deep ?

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(5m × 25cm × 10cm)

7. How many bricks will be required to construct a wall

8m long, 6m high and 22.5 cm thick if each brick

measures ?

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(25cm × 11.25cm × 6cm)

8. Find the capacity of a closed rectangular cistern

whose length is 8 m, breadth 6 m and depth 2.5 m. Also,

find the area of the iron sheet required to make the

cistern .

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9. A room is 9 m long, 8 m broad and 6.5 m high. It has

one door of dimensions and three

windows each of dimensions Find the

cost of white washing the walls at Rs 3.80 per square

metre.

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2m × 1. 5m

1. 5m × 1m.

10. A wall 15 m long, 30 cm wide and 4m high is made

of bricks, each measuring

. If of the total

volume of the wall consits of mortar, how many bricks

are there in the wall ?

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(22cm × 12.5cm × 7.5cm)1

12

11. How many cubic centimetres of iron are there in an

open box whose external dimensions are 36cm, 25cm

and 16.5cm, the iron being 1.5cm thick throughout? If 1

cubic cm of iron weighs 15g, find the weight of the empty

box in kg.

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12. A box made of sheet metal costs at per

square metre.If the box is long and wide,find its

height

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6480 120

5m 3m

13. The volume of a cuboid is . Its length is

16m, and its breadth and height are in the ratio .

Find the breadth and height of the cuboid.

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1536m3

3 : 2

14. How many person can be accommodated in a dining

hall of dimensions , assuming

that each person requires 5 cubic metres of air ?

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(20m × 16m × 4.5m)

15. A classroom is 10 m long, 6.4 m wide and 5m high. If

each student be given of the floor area, how1.6m2

many students can be accommodated in the room ?

How many cubic metres of air would each student get ?

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16. The surface area of a cuboid is . Its length

and breadth are 14 cm and 11 cm respectively. Find its

height.

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758cm2

17. In a shower, 5 cm of rain falls. Find the volume of

water that falls on 2 heactares land

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18. Find the volume, the lateral surface area, the total

surface area and the diagonal of a cube, each of whose

edges measures 9 m. (Take )

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√3 = 1.73

19. The total surface area of a cube is . Find

its volume

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1176cm2

20. The lateral surface area of a cube is . Find

its volume

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900cm2

21. The volume of a cube is . Its total surface

area is

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512cm3

22. Three cubes of metal with edges 3cm, 4 cm and 5

cm respectively are melted to form a single cube. The

lateral surface area of the new cube formed is

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23. The length of the longest rod that can be placed in a

room of dimensions is(10m × 10m × 5m)

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24. The sum of length, breadth and depth of a cuboid is

and length of its diagonal is Find the

surface area of the cuboid.

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19 cm 11 cm.

25. Each edge of a cube is increased by 50%. Find the

percentage increase in the surface area of the cube.

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26. If is the volume of a cuboid of dimensions

is its surface area, then prove that

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V

a,  b,  c and S

= ( + + )1

V

2

S

1

a

1

b

1

c

27. Water in a canal,

is flowing with a velocity of How many

area will it irrigate in if of standing

water is desired?

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30 dm wide and 12dm deep,

20km per hour.

30 m ∈ , 9 cm

Exercise 15 B

28. A solid metallic cuboid of dimensions

is melted and recast in to solid cubes of

edge 2 m .find the number of cubes so formed.

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9m × 8m × 2

1. The diameter of a cylinder is 28 cm and its height is

40 cm. Find the curved surface area, total surfacce area

and the volume of the cylinder.

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2. A patient in a hospital is given soup daily in a

cylindrical bowl of diameter 7 cm. If the bowl is filled with

soup to a height of 4 cm, how much soup the hospital

has to prepare daily to serve 250 patients?

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3. The pillars of a temple are cylindrically shaped (see

Fig. 13.26). If each pillar has a circular base of radius 20

cm and height 10 m, how much concrete mixture would

be required to build 14 such pillars?

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4. A soft drink is available in two packs - (i) a tin can with

a rectangular base of length 5cm and width 4cm, having

a height of 15cm and (ii) a plastic cylinder with circular

base of diameter 7cm and height 10cm. Which container

has greater capacity and by how much?

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5. There are 20 cylindrical pillars in a building, each

having a diameter of 50 cm and height 4m. Find the cost

of cleaning them at Rs 14 per .

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m2

6. Curved surface area of a right circular cylinder is

. If the radius of the base of the cylinder is

0.7 m, find its height.

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4. 4\ m2

7. If the lateral surface of a cylinder is and its

height is 5 cm, then find(i) radius of its base (ii) its

volume.

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94. 2 cm2

8. The capacity of a closed cylindrical vessel of height

1m is 15.4 litres. How many square metres of metal

sheet would be needed to make it?

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9. The inner diameter of a cylindrical wooden pipe is 24

cm and its outer diameter is 28 cm. The length of the

pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of

wood has a mass of 0.6 g.

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10. In a hot water heating system, there is a cylindrical

pipe of length 28 m and diameter 5 cm. Find the total

radiating surface in the system.

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11. Find the weight of a solid cylinder of radius 10.5 cm

and height 60 cm if the material of the cylinder weight 5g

per

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cm3

12. The curved surface area of a cylinder is

and its diameter is 20 cm. Find its height and volume

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1210cm2

13. The curved surface area of a cylinder is

and the circumference of its base is 110 cm. Find the

4400cm2

height and the volume of the cylinder

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14. The ratio between the radius of the base and the

height of a cylinder si . If its volume is

then its total surface area is

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2 : 3 1617cm3

15. A solid cylinder has total surface area of 462 square

cm. Its curved surface area is one-third of its total

surface area. Find the volume of the cylinder. (Take

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π = 22 / 7)

16. The total surface area of solid cylinder is

and its curved surface area is of the total surface

area. Find the volume of the cylinder.

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231cm2

2

3

17. The ratio between the curved surface area and the

total right circular cylinder is . Find the volume of the

cylinder if its total surface area is 616

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1 : 2

cm2

18. A cylindrical bucket, 28 cm in diameter and 72 cm

heigh, is full of water. The water is emptied into a

rectangular tanke, 66 cm long and 28 cm wide. Find the

height of the water level in the tank.

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19. A barrel of a fountain pen, cylindrical in shape, is 7

cm long and 5mm in diameter. A full barrel of ink in the

pen will be used up when writing 310 words on the

average, if a bottle of ink containing one-fifth of a litre

then the number of words that can be formed is

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20. of gold is drawn into a wire 0.1 mm in

diameter. Find the length of the wire.

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1cm3

21. If of cast iron weights 21g, find the weight of a

cast iron pipe of length 1m with a bore of 3 cm in which

the thickness of the metal is 1cm.

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1cm3

22. A cylindrical tube, open at both ends, is made of

metal. The internal diameter of the tube is 10.4 cm and

its length is 25 cm. The thickness of the metal is 8 mm

everywhere. Calculate the volume of the metal.

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23. It is required to make a closed cylindrical tank of

height 1m and base diameter 140 cm from a metal

sheet. How many square metres of the sheet are

required for the same ?

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24. At a Ramzan Mela, a stall keeper in one of the food

stalls has a large cylindrical vessel of base radius 15 cm

filled up to a height of 32 cm with orange juice. The juice

is filled in small cylindrical glasses (see Fig. 13.27) of

radius 3 cm u

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25. A well with 10m inside diameter is dug 8.4m deep.

Earth taken out of it is spread all around it to a width of

7.5m to form an embankment. Find the height of the

embankment.

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26. How many litres of water flow out of a pipe having an

area of cross-section of in one minute, if the

speed of water in the pipe is ?

5 cm2

30 cm/sec

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27. A cylindrical water tank of diameter 1.4m and height

2.1m is being fed by a pipe of diameter 3.5cm through

which water flows at the rate of 2 metre per second. In

how much time the tank will be filled?

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28. A cylindrical container with diameter of base 56cm

contains sufficient water to submerge a rectangular solid

of iron with dimensions cm cm cm Find the rise

in the level of the water when the solid is completely

submerged.

32 22 14

A. cm

B. cm

C. cm

D. cm

Answer: A

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4

8

2

14

29. Find the cost of sinking a tube-well 280 m deep,

having a diameter 3m at the rate of Rs 15 per cubic

metre. Find also the cost of cementing its inner curved

surface at Rs 10 per square metre.

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30. Find the length of 13.2 kg of copper wire of diameter

4 mm, when 1 cubic centimetre of copper weights 8.4 g.

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31. It costs Rs 3300 to paint the inner curved surface of

a cylindrical vessel 10m deep at the rate of Rs 30 per

. Find the

(i) inner curved surface area of the vessel,

(ii) inner radius of the base, and

(iii) capacity of the vessel

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m2

32. The difference between inside and outside surfaces

of a cylindrical tube 14cm long is 88sq. cm. If the volume

of the tube is 176 cubic cm, find the inner and outer radii

of the tube.

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33. A rectangular sheet of paper can be

transformed into the curved surface of a right circular

cylinder in two ways namely, either by rolling the paper

along its length or by rolling it along its breadth. Find the

ratio of the volume of the two cylinders, thus formed.

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30cm × 18cm

Exercise 15 C

1. Find the curve surface area of a cone with base

radius 5.25 cm and slant height 10 cm

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2. Find the total surface area of a cone, if its slant height

is 21cm and diameter of its base is 24 cm

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3. A joker's cap is in the form of a right circular cone of

base radius 7 cm and height 24 cm. Find the area of the

sheet required to make 10 such caps.

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4. The curved surface area of a cone is and its

slant height is 14 cm. Find the radius of the base and

total surface area of the cone.

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308cm2

5. The slant height and base diameter of a conical tomb

are 25 m and 14 m respectively. Find the cost of

whitewashing its curved surface at the rate of Rs 12 per

.

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m2

6. A conical tent is 10m high and the radius of its base is

24 m. Find the slant height of the tent. If the cost of

canvas is Rs 70, find the cost of canvas required to

make the tent.

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1m2

7. A bus stop is barricated from the remaining part of the

road by using 50 hollow cones made of recycled

cardboard. Each one has a base diameter of 40 cm and

height 1m. If the outer side of each of the cones is to be

painted and the cost of painting is Rs 25 per , whatm2

will be the cost of painting all these cone ? (Use

)

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π = 3.14 and √1.04 = 1.02

8. Find the volume, cuved surface area and the total

surface area of a cone having base radius 35 cm and

height 12 cm

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9. Find the volume, curved surface area and the total

surface area of a cone whose height is 6 cm and slant

height 10 cm. (Take )

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π = 3.14

10. A conical pit of diameter 3.5 m is 12 m deep. What is

its capacity in kilolitres ?

HINT kilolitre

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1m3 =

11. A heap of wheat is in the form of a cone of diameter

9m and height 3.5m. Find its volume. How much canvas

cloth is required to just cover the heap?

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(Use π = 3. 14)

12. A man uses a piece of canvas having an area of

, to make a conical tent of base radius 7m.

Assuming that all the stitching margins and wastage

incurred while cutting, amount to approximately ,

find the volume of the tent that can be made with it.

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551m2

1m2

13. How much cloth 2.5 m wide will be required to make

a conical tent having base radius 7 m and height 24 m ?

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14. Two cones have their heights in the ratio and

the radii of their bases in the ratio . Show that their

volumes are in the ratio

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1 : 3

3 : 1

3 : 1

15. A cylinder and a cone have equal radii of their bases

and equal heights. If their curved surface areas are in

the ratio 8:5, show that the radius of each is to the

height of each as 3:4.

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16. A right circular cone is 3.6 cm high and radius of its

base is 1.6 cm. It is melted and recast into a right

circular cone with radius of its base as 1.2 cm. Find its

height.

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17. A circus tent is cylindrical to a height of metres and

conical above it. If its diameter is 105 m and the slant

height of the conical portion is m, calculate the length

of the canvas m wide to make the required tent.

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3

53

5

18. A iron pillar consists of a cylindrical portion 2.8 m

high and 20 cm in diameter and a cone 42 cm heigh is

surmounting it. Find the weight of the pillar, given that

of iron weight 7.5 g

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1cm3

19. From a solid right circular cylinder with height 10 cm

and radius of the base 6 cm, a right circular cone of the

same height and base is removed. Find the volume of

the remaining solid. (Take )

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π = 3.14

20. Water flows at the rate of 10 meter per minute

through a cylindrical pipe having diameter as 5 mm. How

much time will it take to fill a conical vessel whose

diameter of base is 40 cm and depth 24 cm?

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21. A colth having an area of is shapped into the

form of a conical tent of radius 5 m.

(i) How many students can sit in the tent, if a student on

an average occupies on the ground ?

(ii) Find the volume of the cone.

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165m2

m25

7

Exercise 15 D

1. Find the volume and surface area of a sphere whose

radius is:

(i) 3.5 cm (ii) 4.2 cm (iii) 5 cm

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2. The volume of a sphere is . Find its radius

and hence its surface area

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38808cm3

3. Find the surface area of a sphere whose volume is

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60.375m3

4. Find the volume of a sphere whose surface area is

154

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cm2

5. The surface area of sphere is . Find its

volume

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(576π)cm2

6. How many lead shots, each 3mm in diameter, can be

made from a cuboid with dimensions

?

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(12cm × 11cm × 9cm)

7. How many lead balls, each of radius 1 cm, can be

made from a sphere of radius 8 cm ?

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8. A solid sphere of radius 3 cm is melted and then cast

into smaller spherical balls, each of diameter 0.6 cm.

Find the number of small balls thus obtained.

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9. A metallic sphere of radius 10.5 cm is melted and

then recast into smaller cones, each of radius 3.5 cm

and height 3 cm. How many cones are obtained ?

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10. How many sphere 12 cm in diameter can be made

from a metallic cylinder of diameter 8 cm and height 90

cm ?

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11. The diameter of a sphere is 6 cm. It is melted and

drawn into a wire of diameter 2 mm. The length of the

wire is

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12. The diameter of a copper sphere is 18 cm. It is

melted and drawn into a long wire of uniform cross

section. If the length of the wire is 108 m, find its

diameter.

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13. A sphere of diameter 15.6 cm is melted and cast into

a right circular cone of height 31.2 cm. Find the diameter

of the base of the cone.

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14. A spherical cannonball 28 cm in diameter is melted

and cast into a right circular cone mould, whose base is

35 cm in diameter. Find the height of the cone.

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15. A spherical ball of radius 3 cm is melted and recast

into the spherical balls. The radii of two of these balls

are 1.5 cm and 2 cm. Find the radius of the third balls.

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16. The radii of two spheres are in the ratio . Find

the ratio of their surface areas.

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1 : 2

17. The surface areas of two spheres are in the ratio

. Find the ratio of their volumes.

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1 : 4

18. A cylindrical tub of radius 12 cm contains water to a

depth of 20 cm. A spherical iron ball is dropped into the

tub and thus the level of water is raised by 6.75 cm.

What is the radius of the balls ?

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19. A cylindrical bucket with base radius 15 cm is filled

with water up to a height of 20 cm. A heavy iron

spherical ball of radius 9 cm is dropped into the bucket

to submerge completely in the water. Find the increase

in the level of water.

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20. The outer diameter of a spherical shell is 12 cm and

its inner diameter is 8 cm. Find the volume of metal

contained in the shell. Also, find its outer surface area.

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21. A hollow spherical shell is made of a metal of density

4.5 g per . If its internal and external radii are 8 cm

and 9 cm respectively, find the weight of the shell.

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cm3

22. A hemisphere of lead of radius 9 cm is cast into a

right circular cone of height 72 cm. Find the radius of the

base of the cone.

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23. A hemispherical bowl of internal radius 9 cm

contains a liquid. This liquid is to the filled into cylindrical

shaphed small bottles of diameter 3 cm and height 4 cm.

How many bottles are required to empty the bowl ?

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24. a hemispherical bowl is made of steel 0.5 cm thick.

The inside radius of the bowl is 4 cm. Find the volume of

steel used in making the bowl.

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25. A hemispherical bowl is made of steel, 0.25 cm thick.

The inner radius of the bowl is 5 cm. Find the outer

curved surface area of the bowl.

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26. A hemispherical bowl made of brass has inner

diameter 10.5 cm. Find the cost of tin-plating it on the

inside at the rate of Rs 32 per .

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100cm2

Multiple Choice Questions Mcq

27. The diameter of the moon is approximately one

fourth of the diameter of the earth. What fraction of the

volume of the earth is the volume of the moon?

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28. Volume and surface area of a solid hemisphere are

numerically equal. What is the diameter of the

hemisphere. ?

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1. The length, breadth and height of a cuboid are 15 cm,

12 cm and 4.5 cm respectively. Its volume is

A.

B.

C.

D.

Answer: C

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243cm3

405cm3

810cm3

603cm3

2. A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its

total surface area is

A.

B.

C.

D.

Answer: B

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864cm2

552cm2

432cm2

276cm2

3. The length, breadth and height of a cuboid are 15m,

6m and 5dm respectively. The lateral surface area of the

cuboid is

A.

B.

45m2

21m2

C.

D.

Answer: B

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201m2

90m2

4. A beam 9 m long, 40 cm wide and 20 cm high is

made up of iron which weight 50kg per cubic metre. The

weight of the beam is

A. 27 kg

B. 48 kg

C. 36 kg

D. 56 kg

Answer: C

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5. The length of the longest rod that can be placed in a

room of dimensions is

A. 15m

B. 16m

C.

D. 12 m

Answer: A

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(10m × 10m × 5m)

10√5m

6. What is the maximum length of a pencil that can be

placed in a rectangular box of dimensions

? (Given )

A. 8 cm

B. 9.5 cm

C. 19 cm

D. 11.2 cm

Answer: D

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(8cm × 6cm × 5cm) √5 = 2.24

7. The number of planks of dimensions

that can be stored in a pit which is(4m × 5m × 2m)

40 m long, 12m wide and 16m deep, is

A. 190

B. 192

C. 184

D. 180

Answer: B

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8. How many planks of dimensions

can be stored in a pit which is

20m long, 6m wide and 50 cm deep ?

A. 480

(5m × 25cm × 10cm)

B. 450

C. 320

D. 360

Answer: A

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9. How many bricks will be required to construct a wall

8m long, 6m high and 22.5 cm thick if each brick

measures ?

A. 4800

B. 5600

C. 6400

(25cm × 11.25cm × 6cm)

D. 5200

Answer: C

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10. How many persons can be accommodated in a

dining hall of dimensions ,

assuming that each person requires of air ?

A. 250

B. 270

C. 320

D. 300

Answer: B

(20m × 15m4.5m)

5m3

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11. A river 1.5 m deep and 30 m wide is flowing at the

rate of 3km per hour. The volume of water that rums into

the sea per minute is

A.

B.

C.

D.

Answer: B

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2000m3

2250m3

2500m3

2750m3

12. The lateral surface area of a cube is . The

volume of the cube is

A.

B.

C.

D.

Answer: D

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256m2

64m3

216m3

256m3

512m3

13. The total surface area of a cube is . The

volume of the cube is

A.

96m2

8cm3

B.

C.

D.

Answer: C

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27cm3

64cm3

512cm3

14. The volume of a cube is . Its total surface

area is

A.

B.

C.

D.

512cm3

256cm2

384cm2

512cm2

64cm2

Answer: B

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15. The length of the longest rod that can fit in a cubical

vessel of side 10 cm, is

A. 10 cm

B. 20 cm

C.

D.

Answer: D

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10√2cm

10√3cm

16. If the length of diagonal of a cube is cm then its

surface area is

A.

B.

C.

D.

Answer: B

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8√3

192cm2

384cm2

512cm2

768cm2

17. If each edge of a cube is increased by %, the

percentage increase in its surface area is

50

A. %

B. %

C. %

D. %

Answer: D

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75

105

120

125

18. Three cubes of metal with edges 3cm, 4 cm and 5

cm respectively are melted to form a single cube. The

lateral surface area of the new cube formed is

A.

B.

72cm2

144cm2

C.

D.

Answer: B

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128cm2

256cm2

19. In a shower, 5 cm of rain falls. Find the volume of

water that falls on 2 heactares land

A.

B.

C.

D.

Answer: D

500m3

750m3

800m3

1000m3

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20. Two cubes have their volume in the ratio . The

ratio of their surface areas is

A.

B.

C.

D.

Answer: C

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1 : 27

1 : 3

1 : 8

1 : 9

1 : 18

21. If each side of a cube is doubled then its volume

A. is doubled

B. becomes 4 times

C. becomes 6 times

D. becomes 8 times

Answer: D

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22. The diameter of the base of a cylinder is 6 cm and its

height is 14 cm. The volume of the cylinder is

A. 198cm3

B.

C.

D.

Answer: B

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396cm3

495cm3

297cm3

23. If the diameter of a cylinder is 28 cm and its height is

20 cm then its curved surface area is

A.

B.

C.

D.

880cm2

1760cm2

3520cm2

2640cm2

Answer: B

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24. If the curved surface area of a cylinder is

and its base radius is 14 cm then its height is

A. 10 cm

B. 15 cm

C. 20 cm

D. 40 cm

Answer: C

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1760cm2

25. The height of a cylinder is 14 cm and its curved

surface area is . The volume of the cylinder is

A.

B.

C.

D.

Answer: B

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264cm2

308cm3

396cm3

1232cm3

1848cm3

26. The surved surface area of a cylindrical pillar is 264

and its volume is 924 . The height of the pillar ism2 m3

A. 4 m

B. 5 m

C. 6 m

D. 7m

Answer: C

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27. The ratii of two cylinder area in the ratio and

their heights are in the ratio . The ratio of their

curved surface area is

A.

B.

2 : 3

5 : 3

2 : 5

8 : 7

C.

D.

Answer: C

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10 : 9

16 : 9

28. The ratii of two cylinders are in the ratio and

their heights are in the ratio . The ratio of their

volumes is

A.

B.

C.

D.

2 : 3

5 : 3

27 : 20

20 : 27

4 : 9

9 : 4

Answer: B

Watch Video Solution

29. The ratio between the radius of the base and the

height of the cylinder is 2:3. If its volume is 1617 ,

the total surface area of the cylinderical is

A.

B.

C.

D.

Answer: D

Watch Video Solution

cm3

308cm2

462cm2

540cm2

770cm2

30. Two circular cylinders of equal volume have their

heights in the ratio . The ratio of their radii is

A.

B.

C.

D.

Answer: B

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1 : 2

1 : √2

√2 : 1

1 : 2

1 : 4

31. The ratio between the curved surface area and the

total surface area of a right circular cylinder is . If the1 : 2

total surface area is then the volume of the

cylinder is

A.

B.

C.

D.

Answer: A

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616cm2

1078cm3

1232cm3

1848cm3

924cm3

32. In a cylinder, if the radius is halved and the height is

doubled then the volume will be

A. the same

B. doubled

C. halved

D. four times

Answer: C

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33. The number of coins 1.5 cm in diameter and 0.2 cm

thick to be melted to form a right circular cylinder of

height 10 cm and diameter 4.5 cm is

A. 540

B. 450

C. 380

D. 472

Answer: B

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34. The radius of a wire is decreased to one-third. If

volume remains the same, the length will become

A. 2 times

B. 3 times

C. 6 times

D. 9 times

Answer: D

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35. The diameter of a roller, 1 m long, is 84 cm. If it

takes 500 complete revolutions to level a playground,

the area of the playground is

A.

B.

C.

D.

Answer: B

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1440m2

1320m2

1260m2

1550m2

36. 2.2 cubic dm of brass is to be drawn into a cylindrical

wire 0.50 cm in diameter. Find the length of the wire.

A. 110 m

B. 112 m

C. 98 m

D. 124 m

Answer: B

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37. The lateral surface area of a cylinder is

A. πr2h

B.

C.

D.

Answer: C

Watch Video Solution

πrh

2πrh

2πr2

38. The height of a cone is 24 cm and the diameter of its

base is 14 cm. The curved surface area of the cone is

A.

B.

C.

D.

528cm2

550cm2

616cm2

704cm2

Answer: B

Watch Video Solution

39. The volume of a right circular cone of height

and base radius is

A.

B.

C.

D.

Answer: D

Watch Video Solution

12cm

6cm,

(12π)cm3

(36π)cm3

(72π)cm3

(144π)cm3

40. How much cloth 2.5 m wide will be required to make

a conical tent having base radius 7 m and height 24 m ?

A. 120 m

B. 180 m

C. 220 m

D. 550 m

Answer: C

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41. The volume of a cone is and its height is

15 cm. What is the radius of the cone ? (Use )

1570cm3

π = 3.14

A. 10 cm

B. 9 cm

C. 12 cm

D. 8.5 cm

Answer: A

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42. The height of a cone is 21 cm and its slant height is

28 cm. The volume of the cone is

A.

B.

C.

7356cm3

7546cm3

7506cm2

D.

Answer: B

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7564cm3

43. The volume of a right circular cone of height 24 cm is

. Its curved surface area is

A.

B.

C.

D.

Answer: C

Watch Video Solution

1232cm3

1254cm2

704cm2

550cm2

462cm2

44. If the volume of two cones be in the ratio and

the ratii of their bases be in the ratio then the ratio

of their heights is

A.

B.

C.

D.

Answer: D

Watch Video Solution

1 : 4

4 : 5

1 : 5

5 : 4

25 : 16

25 : 64

45. If the height of a cone is doubled then its volume is

increased by

A. 1

B. 2

C. 3

D. 4

Answer: A

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46. The curved surface area of one cone is twice that of

the other while the slant height of the latter is twice that

of the former. The ratio of their radii is

A.

B.

C.

D.

Answer: B

Watch Video Solution

2 : 1

4 : 1

8 : 1

1 : 1

47. The ratio of the volumes of a right circular cylinder

and a right circular cone of the same base and the same

height will be

A.

B.

1 : 3

3 : 1

C.

D.

Answer: B

Watch Video Solution

4 : 3

3 : 4

48. A right circular cylinder and a right circular cone

have the same radius and the same volume. The ratio of

the height of the cylinder to that of the cone is

A.

B.

C.

D.

3 : 5

2 : 5

3 : 1

1 : 3

Answer: D

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49. The radii of the bases of a cylinder and a cone are in

the ratio and their heights are in the ratio .

Then, their volumes are in the ratio

A.

B.

C.

D.

Answer: A

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3 : 4 2 : 3

9 : 8

8 : 9

3 : 4

4 : 3

50. If the height and the radius of a cone are doubled,

the volume of the cone becomes

A. 3 times

B. 4 times

C. 6 times

D. 8 times

Answer: D

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51. A solid metallic cylinder of base radius 3 cm and

height 5 cm is melted to make n solid cones of height 1

cm and base radius 1 mm. The value of n is

A. 450

B. 1350

C. 4500

D. 13500

Answer: D

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52. A conical tents is to accommodate person such

that each person occupies of space on the ground.

They have of air to breathe. The height of the

cone is

11

4m2

220m3

A.

B.

C.

D.

Answer: B

Watch Video Solution

14m

15m

16m

20m

53. The volume of a sphere of radius is

A.

B.

C.

2r

32πr3

316πr3

38πr3

3

D.

Answer: A

Watch Video Solution

64πr3

3

54. The volume of a sphere of radius is

A.

B.

C.

D.

Answer: B

Watch Video Solution

10.5cm

9702cm3

4851cm3

19494cm3

14553cm3

55. The surface area of a sphere of radius is

A.

B.

C.

D.

Answer: D

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21cm

2772cm2

1386cm2

4158cm2

5544cm2

56. The surface area of a sphere is . Its

volume is

A.

1386cm2

1617cm3

B.

C.

D.

Answer: C

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3234cm3

4158cm2

9702cm2

57. If the surface area of a sphere is then its

volume is

A.

B.

C.

D.

(144π)m2

(288π)m3

(188π)m3

(300π)m3

(316π)m3

Answer: A

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58. The volume of a sphere is . Its curved

surface area is

A.

B.

C.

D.

Answer: A

Watch Video Solution

38808cm3

5544cm2

8316cm2

4158cm2

1386cm2

59. If the ratio of the volumes of two spheres is then

the ratio of their surface areas is

A.

B.

C.

D.

Answer: B

Watch Video Solution

1 : 8

1 : 2

1 : 4

1 : 8

1 : 16

60. A solid metal ball of radius 8 cm is melted and cast

into smaller balls, each of radius 2 cm. The number of

such balls is

A. 8

B. 16

C. 32

D. 64

Answer: D

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61. A cone is 8.4 cm heigh and the radius of its base is

2.1 cm. It is melted and recast into a sphere. The radius

of the sphere is

A. 4.2 cm

B. 2.1 cm

C. 2.4 cm

D. 1.6 cm

Answer: B

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62. A solid lead ball of radius is melted and then

drawn into a wire of diameter The length of

wire is

A.

B.

C.

D.

6 cm

0.2 cm.

272m

288m

292m

296m

Answer: B

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63. A metallic sphere of radius is melted and

then react into small cones, each of radius and

height The number of such cones will be

A.

B.

C.

D.

Answer: C

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10.5 cm

3.5 cm

3 cm.

21

63

126

130

64. How many lead shots, each in diameter, can

be made from a cuboid of dimensions

?

A.

B.

C.

D.

Answer: D

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0.3cm

9cm × 11cm × 12cm

7200

8400

72000

84000

65. The diameter of a sphere is It is melted and

drawn into a wire of diameter The length of the

wire is

A.

B.

C.

D.

Answer: C

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6cm.

2mm.

12m

18m

36m

66m

66. A sphere of diameter is melted and cast

into a right circular cone of height The radius

12.6cm

25.2cm.

of the base of the cone is

A.

B.

C.

D.

Answer: A

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6.3cm

2.1cm

6cm

4cm

67. A spherical ball of radius is melted and recast

into three spherical balls. The radii of two of these balls

are and The radius of the third ball is

A.

3cm

1.5cm 2cm.

1cm

B.

C.

D.

Answer: C

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1.5cm

2.5cm

0.5cm

68. The radius of hemispherical balloon increases from

to as air is being pumped into it. The ratio of

the surface areas of the balloons in two cases is

A.

B.

C.

6cm 12cm

1 : 4

1 : 3

2 : 3

D.

Answer: A

Watch Video Solution

1 : 2

69. The volumes of two spheres are in the ratio

and the sum of their radii is The difference in their

total surface area is

A.

B.

C.

D.

Answer: D

64 : 27

7cm.

38cm2

58cm2

78cm2

88cm2

Watch Video Solution

70. A hemispherical bowl of radius contains a

liquid. This liquid is to be filled into cylindrical small

bottles of diameter and height How many

bottles will be needed to empty the bowl ?

A.

B.

C.

D.

Answer: C

Watch Video Solution

9 cm

3 cm 4 cm.

27

35

54

63

71. A cone and a hemisphere have equal bases and

equal volumes. The ratio of their heights is

A.

B.

C.

D.

Answer: B

Watch Video Solution

1 : 2

2 : 1

4 : 1

√2 : 1

72. A cone, a hemisphere and a cylinder stand on equal

bases and have the same height. Show that their

volumes are in the ratio

A.

B.

C.

D.

Answer: A

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1 : 2 : 3

2 : 1 : 3

2 : 3 : 1

3 : 2 : 1

73. If the volume and surface area of a sphere are

numerically the same, then its radius is

A. 1 unit

B. 2 unit

C. 3 units

Solved Examples

D. 4 units

Answer: C

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1. Find the volume, the total surface area and the lateral

surface area of a cuboid which is long, wide

and high.

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15m 12m

4.5m

2. How many bricks will be required to construct a wall

long, high and thick ? It is being

given that each brick measured

?

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13.5m 6m 22.5cm

(27cm × 12.5cm × 9cm)

3. A room is long, wide and high. If has

two doors, each of dimensions and the

three windows, each of dimensions .

Find the cost of distempering the walls of the room from

inside at the rate of per square metre.

Watch Video Solution

16m 9m 3m

(2m × 1.5m)

(1.6m × 75cm)

Rs50

4. A field is 70 m long and 40 m broad. In one corner of

the field, a pit which is 10 m long, 8 m broad and 5 m

deep, has been dug out. The earth taken out of it is

evenly spread over the remaining part of the field. Find

the rise in the level of the field.

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5. An open wooden box long, wide and

high, is made of thick wood.

Find (i) the capacity of the box, (ii) volume of wood used

and (iii) weight of the box, it being given that 100 of

wood weight

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80cm 65cm

45cm 2.5cm

cm3

8g

6. Find the volume, total surface area, lateral surface

area and the length of diagonal of a cube, each of

whose edges measured

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20cm

7. The total surface area of a cube is . Find the

volume

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216cm2

8. The lateral surface area of a cube is . Find its

volume and the total surface area

W h Vid S l i

324cm2

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9. How many square sheets of coloured paper of side 30

cm would be required to cover a wooden box having

length, breadth and height as 90 cm, 60 cm and 30 cm

respectively ?

A.

B.

C.

D.

Answer: A

Watch Video Solution

22

23

24

25

10. A small indoor greenhouse (herbarium) is made

entirely of glass panes (including base) held together

with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass? (ii) How much of tape is

needed for all the 12 edge

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11. A sweet seller placed an order for making cardboard

boxes of two sizes, namely

. If 5% of the total surface area is required extra for all

overlaps and the cost of the cardboard is Rs 5 for

, find the cost of cardboard required for 200

boxes of each kind.

(25cm × 20cm × 5cm) and (15cm × 12cm × 5cm)

1000cm2

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12. Ravish wanted to make a temporary shelter for his

car by making a box-like structure with tarpaulin that

covers all the four sides and the top of the car (with the

front face as a flap which can be rolled up). Assuming

that the stitching margins are very small, and therefore

negligible, how much tarpaulin would be required to

make the shelter of height 2.5 metre with base

dimension

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4m x 3m  ?

13. A cubical box has each edge and another

cuboidal box is long, wide and

high.

(i) Which box has the greater lateral surface area and by

how much?

(ii) Which box has the smaller total surface area and by

how much?

Watch Video Solution

10cm

12.5cm 10cm 8cm

14. Hameed has built a cubical water tank with lid for his

house, with each outer edge 1.5 m long. He gets the

outer surface of the tank excluding the base, covered

with square tiles of side 25 cm (see Fig. 13.5). Find how

much he would spend for the

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15. A solid cube of side is cut into 8 cubes of

equal volume. What will be the side of the new cube?

Also, find the ratio between their surface areas.

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12cm

16. A river deep and wide is flowing at the rate

of per hour. How much water will fall into the sea in

a minute?

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3m 40m

2km

17. The length of a cold storage is double its breadth. Its

height is m. The area of its four walls (including doors)

is . Find its volume.

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3

108 m2

18. A village, having a population of 4000, requires 150

litres of water per head per day. It has a tank measuring

. For how

many days will the water of this tank last?

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20\ m\ × \ 15\ m\ × \ 6\ m

19. A room is half as long again as it is broad. The cost

of carpeting the room at per is and

the cost of papering the walls at per is

If door and window occupy , find find

dimensions of the room

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Rs13 m2 Rs702

Rs7 m2

Rs1204. 1 2 8m2

20. Water flows in a tank at the base

through a pipe whose cross section is by

at the speed of per hour. In what time will the

water be metres deep ?

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60m × 40m

2dm 1.5dm

8km

5

21. A storage tank is in the form of a cube . When it is

full of water, the volume of water is . If the

present depth of water is then, find the volume of

water already used from the tank.

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15.625m3

1.3m,

22. Find the (i) Volume,

(ii) Area of curved surface and

(iii) Total surface area of a cylinder having radius of the

base and height

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14cm 30cm.

23. The total surface area of a cylinder of radius is

.

Find the height and the volume of the cylinder

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7cm

880cm2

24. The curved surface area and the volume of a pillar

are respectively. Find the

diameter and the height of the pillar.

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264m2 and 396m3

25. How many cubic metres of earth must be dug out to

sink a well deep and having a radius of If the14m 4m.

earth taken out is spread over a plot of dimension

. What is the height of the platform so

formed?

Watch Video Solution

(25m × 16m)

26. A well of inner diameter 14m is dug to a depth of

15m. Earth taken out of it has been evenly spread all

around it to a width of 7m to form an embankment. Find

the height of the embankment so formed.

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27. The diameter of a roller, long, is If it

takes complete revolutions to level a playground,

120cm 84cm.

500

find the cost of leveling it at per square metre.

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Rs5

28. Find the number of coins in diameter and

thick to be melted to form a right circular cylinder

of height and diameter

Watch Video Solution

1.5cm

0.2cm

5cm 4.5cm.

29. 2.2 cubic dm of brass is to be drawn into a cylindrical

wire 0.50 cm in diameter. Find the length of the wire.

Watch Video Solution

30. The external diameter of a lead pipe is and

the thickness of the lead is Find the weight of a

pipe of length , it being given that of lead

weight

Watch Video Solution

2.4cm

2mm.

7m 1cm3

10g.

31. An iron pipe long has exterior diameter equal

to If the thickness of the pipe is find the

whole surface of the pipe.

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20cm

25cm. 1cm,

32. The difference between the outside and inside

surfaces of a cylindrical metallic pipe long is 14cm

. If the pipe is made of of metal, find the

outer and inner radii of the pipe.

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44cm2 99cm3

33. A solid iron rectangular block of dimensions

is cast into a hollow cylindrical

pipe of internal radius and thickness Find

the length of the pipe

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(2.2m × 1.2m × 1m)

35cm 5cm.

34. A copper wire of diameter is evenly wrapped

on a cylinder of length and diameter to

cover its whole surface. Find the length and volume of

6mm

15cm 49cm

the wire. If the specific gravity of copper be per cu

cm, find the weight of the wire.

Watch Video Solution

9g

35. In Fig. 13.12, you see the frame of a lampshade. It is

to be covered with a decorative cloth. The frame has a

base diameter of 20 cm and height of 30 cm. A margin

of 2.5 cm is to be given for folding it over the top and

bottom of the frame. Find

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36. The sum of radius of the base and height of a

cylinder is If the total surface area of the cylinder37m.

is , find the curved surface area and volume of

the cylinder

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1628m2

37. A metal pipe is long. The inner diameter of a

cross section is , the outer diameter being

Find its (i) inner curved surface area

(ii) outer curved surface area

(iii) total surface area

Watch Video Solution

77cm

4cm 4.4cm.

38. Rainwater, which falls on a flat rectangular rooftop of

dimensions by , is transferred into a22m 10m

cylindrical vessel of internal radius through a

circular pipe. A certain day recorded a rainfall of

Find the (i) volume and (ii) height of the water,

filled in the cylindrical vessel.

Watch Video Solution

50cm

2.5cm.

39. Find the lateral curved surface area of a cylindrical

petrol storage tank that is in diameter and

high. How much steel was actually used, if of steel

actually used was wasted in making the closed tank?

Watch Video Solution

4.2m 4.5m

1

12

40. Find the area of the chart paper used to make the

curved surface of a model of cylindrical kaleidoscope of

length cm and radius cm

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25 3.5

41. How much cardboard is required to make 35

penholders in the shape of cylinders, each of radius 3

cm and height 10.5 cm ?

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42. A rectangular sheet of paper, is

rolled along its length of form a cylinder. Find the volume

44cm x 20cm,

of the cylinder so formed.

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43. The radii of two cylinders are in the ratio 2:3 and

their heights are in the ratio 5:3. Calculate the ratio of

their volumes and the ratio of theri curved surfaces.

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44. The volume of a metallic cylindrical pipe is .

Its length is 14 cm and its external radius is 9 cm. Find

its thickness

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784cm3

45. A lead pencil consists of a cylinder of wood with a

solid cylinder of graphite filled in the interior. The

diameter of the pencil is 7 mm and the diameter of the

graphite is 1 mm. If the length of the pencil is 14 cm, find

the volume of the wood

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46. 30 circular plantes, each of radius 14 cm and

thickness 3 cm are placed one above the another to

from a cylindrical solid . Find

(i) the total surfce area.

(ii) volume of the cylinder so formed.

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47. The height of a cone is 24 cm and the diameter of its

base is 14 cm. Find the slant height, volume, area of

curved surface and the cone

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48. How many metres of cloth 5m wide will be required

to make a conical tent, the radius of whose base is 7m

and whose height is 24m?

Watch Video Solution

(Takeπ = )22

7

49. The height of a cone is 21 cm and its slant height is

28 cm. The volume of the cone is

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50. The volume of a right circular cone is . If

the diameter of the base is , find:

(i) height of the cone.

(ii) slant height of the cone.

(iii) curved surface area of the cone.

Watch Video Solution

9856 cm3

28cm

51. The radius and the height of a right circular cone are

in the ratio of and its volume is 2512 cu cm. Find

the curved surface area and the total surface area of the

cone. (Use )

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5 : 12

π = 3.14

52. A cone of height has a curved surface area

square metres. Find its volume. (Take )

Watch Video Solution

8m

188.4 π = 3.14

53. What length of tarpaulin 3m wide will be required to

make a conical tent of height 8m and base radius 6m?

Assume that the extra length of material will be required

for stitching margins and wastage in cutting is

approximately 20 cm

Watch Video Solution

(Use π = 3. 14)

54. A corn cob (see in figure), shaped somewhat like a

cone, has the radius of its broadest end as 2.1 cm and

length as 20cm. If each of the surface of the cob

carries an average of four grains, find how many grains

you would find on the entire cob?

Watch Video Solution

1 cm2

55. A tent is in the form of a right circular cylinder

surmounted by a cone. The diameter of cylinder is 24 m.

The height of the cylindrical portion is 11 m while the

vertex of the cone is 16 m above the ground. Find the

area of canvas required for the tent.

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56. A right triangle ABC with its sides 5 cm, 12cm and

13cm is revolved about the side 12cm. Find the volume

of the solid so formed. If the triangle ABC is revolved

about side 5cm, then find the volume of the solid so

obtained. Find also the ratio of the volumes of the two

solids obtained.

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57. A semicircular sheet of diameter 28 cm is bent to

form an open conical cup. Find the capacity of the cup.

(Use )

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√3 = 1.732

58. A conical tent is to accommodate 11 persons. Each

persons must have 4 sq. metres of the space on the

ground and 20 cubic metrs of air to breath. Find the

height of the cone.

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59. A cylinder is within the cube touching all the vertical

faces. A cone is inside the cylinder. If their heights are

same with the same base, find the ratio of their volumes.

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60. Find the volume of the largest right circular cone that

can be cut out of a cube whose edge is 21 cm

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61. The height of a cone is 30 cm. A small cone is cut off

at the top by a plane parallel to the base. If its volume be

of the volume of the given cone, at what height

above the base is the section mode?

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1

27

62. Find the volume and surface area of a sphere of

radius

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21cm.

63. Find the surface area of a sphere whose volume is

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4851cm3

64. The surface area of a sphere is ,

calculate its radius and the volume.

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346.5 cm2

65. How many spherical bullets can be made out of a

solid cube of lead whose edge measures each

being in diameter.

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44cm,

4cm

66. The diameter of a metallic sphere is The

sphere is melted and drawn into a wire of uniform cross-

section. If the length of the wire is , find its radius.

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6cm.

36m

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67. A metallic sphere of radius is dropped into a

cylindrical vessel, which is partly, filled with water. The

diameter of the vessel is If the sphere is

completely submerged, find by how much the surface of

water will rise.

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21cm

1.68m.

68. A hollow sphere of internal and external diameters

and respectively is melted into a cone of

base diameter Calculate the height of the cone.

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4cm 8cm

8cm.

69. Find the volume, curved surface area and the total

surface area of a hemisphere of diameter

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7cm.

70. The internal and external diameter of a hollow

hemispherical vessel are 20 cm and 28 cm respectively.

Find the cost of painting the vessel all over at 35 paise

by

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cm2

71. On increasing the radius of a sphere by find

the percentage increase in its volume.

10 % ,

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72. The surface area of a sphere of radius is five

times the curved surface area of a cone of radius

Find the height and volume (correct to two decimal

places) of the cone.

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5cm

4cm.

73. If volumes of two spheres are in the ratio

then the ratio of their surface areas is

Watch Video Solution

64 : 27

74. A sphere and a right circule cylinder of the same

radius have equal volume. By what percentage does the

diameter of the cylinder exceed its height ?

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75. The water for a factory is stored in a hemispherical

tank whose internal diameter is . The tank contains

of water. Water is pumped into the tank to fill to its

capacity. Calculate the volume of water pumped into the

tank.

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14m

50L

76. A shopkeeper has one spherical laddoo of radius

With the same amount of material. How many

laddoos of radius can be made ?

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5cm.

2.5cm

77. A shot-putt is a metallic sphere of radius If

the density of the metal is , find the

mass of the shot-putt

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4.9cm.

7.8g per cm3

78. Tow solid spheres made of the same metal have

weight and respectively. Determine the5920g 740g,

radius of the radius of the larger sphere, if the diameter

of the smaller one is

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5cm.

79. A hemispherical tank is made up of an iron sheet

thick. If the inner radius is , then find the

volume of the iron used to make the tank

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1cm 1m