surface area and volumes

Made By: Saurav Kumar Singh Class: IX – F

SURFACE AREA AND

VOLUMES

1) A cylindrical glass can contain 108π cm3 of water. The base of the glass has a radius of 3 cm. What is the height

of the glass?

(a)12 cm (b) 6 cm(c) 9cm (d) 3 cm

The correct answer is 12 cm.Solution:

The base of the cylindrical glass has a radius = 3 cm

Area of the base will be πr²= 9π cm²

Volume of the cylindrical glass = πr²h

The height of the cylindrical glass =  v/πr² = 108π/9π = 12 cm.

The correct option is (A).

2) A silver gift box is cuboidal in shape. The dimensions of the box are 6 cm, 

4 cm and 5 cm. What will be the volume of the gift box?

(a) 24 cm² (b) 24cm³

(c) 120 cm² (d) 120cm³

The correct answer is 120cm³

Solution:

Length of the cuboidal gift box = 6cm

Width of the cuboidal gift box = 4cm

Height of the cuboidal gift box = 5cm

The volume of the gift box = length × width × height

= 6cm*4cm*5cm = 120cm³.

The correct option is (d).

3) The volume of a rectangular prism 10 dm × 4 dm × 2 m is

(a) 800dm (b) 800dm²

(c) 800dm³ (d) 800m

The correct answer is 800dm³

Solution:

Length (l) of the rectangular prism = 10 dm

Width (w) of the rectangular prism = 4 dmHeight (h) of the rectangular prism = 2 m= 2 × 10 dm [10 dm = 1 m] =20dmVolume of the prism = l × w × h10dm*4dm*20dm= 800dm³.The correct option is (c).

4) The cone and a cylinder have a same base area and the same volume, then what is the ratio of their respective

height?

(a) 1:1 (b) 3:1

(c) 4:9 (d) 9:1

The correct answer is 3:1

Solution:

Since the cone and the cylinder have the same base area, their radii are the same.

Therefore, let radius of cone = radius of cylinder= r

Let h1 and h2 be the height of the cone and the cylinder respectively.

Therefore, volume of the cone= 1/3πr²h1

Volume of the cylinder = πr²h2

It is given that the volumes of the cone and the cylinder are equal

Therefore, 1/3πr²h1= πr²h2Þ h1= 3h2 => h1/h2 = 3/1Þ Thus, the ratio of the heights of the cone and the cylinder is 3:1.Þ The correct option is (b).

5) A rectangular box is 16cm high, 10cm long and 5cm broad is to be painted with enamel, What is the total area to be

painted ?

(a) 150cm² (b) 290cm²

(c) 300cm² (d) 580cm²

The correct answer is 580cm²

Solution:

The total area to be painted=the surface area of the rectangular box

= 2(lb + bh + lh).

= 2(10×5 + 5×16 + 10×16).

= 2( 50+ 80+160) = 580cm².

The correct option is (d).

7) A rectangular prism is made by joining some cubes as shown in the figure, the volume of each small cube 1cm³.

(a) 32cm³ (b) 36cm³

(c) 42cm³ (d) 46cm³

The correct answer is 36cm³

Solution:

Length of each side of small cube = 1 cm

Volume of each cube = 1 cm3

The given rectangular prism is made up of 36 small equal sized cubes.

Volume of 36 cubes = 36 × 1 = 36 cm3

Volume of the rectangular prism = volume of 36 cubes = 36 cm3.

The correct option is (b).

8) What is the length of the edge of the cube whose volume is 2744 cm3?

(a) 14cm (b) 12cm

(c) 7cm (d) 6cm

The correct answer is 14cm.

Solution:

Let the length of the edge of the cube be ‘a’.

It is known that volume of cube = (edge)³

Therefore, (a)³ = 2744cm³Þ a = ³√2744cmÞ a = ³√2×2×2×7×7×7cmÞ a = 2×7cm = 14cm.

The correct option is (a).

9) Which of the container has the same volume as the given container ?

The correct answer is figure 2.

This is a simple question so students should try it

self.

10) A box of the shape of a rectangular prism is formed by fitting together 10 cubes. The volume of each cube is 8 cm3.

The volume of the box, so formed is

(a) 50cm³ (b) 60cm³

(c) 70cm³ (d) 80cm³

The correct answer is 80³.

Solution:

Volume of 1 cube = 8 cm3

Number of cubes joined together to form the box = 10

Thus, volume of 10 cubes = 10 × 8 cm3 = 80 cm3

Thus, volume of the box = volume of 10 cubes = 80 cm3

The correct answer is (d).

THE END.