At the end of this lesson, you should be able to:

1. Calculate the volume and capacity of cubes and cuboids 2. Use 1cm3 blocks to work out the volume of cubes and cuboid

3. Working out the depth, length, width of cubes and cuboids

4. Working out the surface area of cubes and cuboids

5. Working out the volume of prisms and cylinders

6. Working out the surface area of spheres, pyramids, cones and composite solids

7. identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms,

cylinders, pyramids, cones and spheres

Worked Example 1

Work out the volume and surface area of the cuboid

Surface Area = _________________

Volume = ______________________

Part 1 – Find the volume of the cuboid

Volume = Length x width x height Volume = 7 x 4 x 3 Volume = 84 cm3

Part 2 – Find the surface area of the cuboid

Step 1 – Work out the area of the 3 faces

Area of face 1 = 3 x 4 = 12cm2 Area of face 2 = 3 x 7 = 21cm2 Area of face 3 = 4 x 7 = 28cm2

Step 2 – Add the areas of the 3 faces together

12cm2 + 21cm2 + 28cm2 = 61 cm2

Step 3 --- Multiply the answer from step 2 by 2

61 x 2 = 122 cm2

Face 1

122 cm2

84 cm3

Topic 7: Volume

Worked Example 2

Work out the volume of the triangular prism

Worked Example 3

Work out the volume the cylinder

Volume = ______________________

Volume = ______________________

Volume = Area of Cross Section x Length

Volume =( 4 x 3

2 ) x 7

Volume = 6 x 7

Volume = 42 Feet3

Volume = πr2h

Volume = π x (2)2 x 4

Volume = 16π or 50.24

42 Feet3

16π in3 or 50.24 in3

Topic 7: Volume

Worked Example 4

Work out the volume the sphere

Worked Example 5

Work out the volume the pyramid

Volume = ______________________

Volume = ______________________

Volume = 4

3 π 𝑟3

Volume = 4

3 x π x 63

Volume = = 4

3 x π x 216

Volume = 288π or 904.32

Volume = 1

3 x base area x height

Volume = 1

3 x ( 8 x 8) x 9

Volume = 1

3 x 9 x 64

Volume = 3 x 64

Volume = 192 cm3

288π m3 or 904.32 m3

192 cm3

Topic 7: Volume

Worked Example 6

Work out the volume of the cone

Worked Example 7

A sphere with a radius of 3cm is melted down and reformed into a solid cone. The cone is 4 cm high.

a. Calculate the radius of the base of the cone. Give your answer in exact form.

Volume = ______________________

Volume = ______________________

Volume = 1

3 π r2 h

Volume = 1

3 x π x 32 x 7

Volume = 1

3 x π x 9 x 7

Volume = 21 π m3

Step 1 – Find Volume of the sphere

V = 4

3 π r3

V = 4

3 x π x 33

V = 4

3 x π x 27

V = 36 π

Step 2 – Find the radius of the cone

V = 1

3 π r2h

36π = 1

3 x π r2 x 4

36 = 1

3 x r2 x 4

108 = 4r2

27 = r2

r = √27

21 π m3

√27 m

Topic 7: Volume

Surface Area formulas you need to know

Cone

Surface area of cone = πr2 + πrL

Topic 7: Volume

Practice Questions

Question 1

Answer = ___________________

Question 2

Answer = _________________

8m

8m

8m

9cm

3cm

12cm

Find the volume of the cuboid

Find the volume of the cube

Topic 7: Volume

Question 3

Answer = _______________

Question 4

Answer: _________________

18mm

18mm

10mm

1 8 m m

10m

Find the volume

of the cube

Find the volume of the cuboid

Topic 7: Volume

Question 5

Count the cubes and find the volume of each cube/cuboid. *Note* 1 Cube is equal to 1 cm3

Answer = ___________ Answer = __________

Answer= ___________ Answer= ___________ Answer= ___________

Answer = __________

Topic 7: Volume

Question 6

The volume of a cuboid is 720cm3

The depth of the cuboid is 8cm

The length of the cuboid is 10cm

Find the width of the cuboid

Answer = ____________________

Answer = ___________ Answer = ___________ Answer = ___________

Topic 7: Volume

Question 7

The volume of a cuboid is 72mm3

The depth of the cuboid is 3mm

The length of the cuboid is 4mm

Find the width of the cuboid

Answer = ______________

Question 8

The volume of a cuboid is 432m3

The width of the cuboid is 9m

The length of the cuboid is 6m

Find the depth of the cuboid

Answer = ___________________

Topic 7: Volume

Question 9

The volume of a cuboid is 231km3

The depth of the cuboid is 11km

The width of the cuboid is 3km

Find the length of the cuboid

Answer = ______________________

Question 10

The volume of a cuboid is 176mm3

The width of the cuboid is 8mm

The length of the cuboid is 11mm

Find the depth of the cuboid

Answer = _____________________

Topic 7: Volume

Question 6

The volume of a cuboid is 784cm3

The depth of the cuboid is 14cm

The length of the cuboid is 7cm

Find the width of the cuboid

Answer = _____________________

Question 7

The volume of a cuboid is 135km3

The depth of the cuboid is 9km

The width of the cuboid is 3km

Find the length of the cuboid

Answer = ___________________

Topic 7: Volume

Question 8

The width of a cuboid is 3cm

The depth of the cuboid is 7cm

The length of the cuboid is 8cm

Find the Volume of the cuboid

Answer = __________________

Question 9

The volume of a cube is 125cm3. Given that the length of this cube is a single digit, Find the:

Depth, width, and length of this cube.

Answer = ____________________

Topic 7: Volume

Question 10

Answer = _________________

Question 11

Answer = ____________

8m

11m

10m

9cm

3cm

12cm

Find the Surface

Area of the

cuboid

Find the

surface area

of the

cuboid

Topic 7: Volume

Question 12

Answer = ________________

Question 13

Answer = ______________

18mm

10mm

1 8 m m

10m

Find the Surface

Area of the cube

Find the Surface

Area of the

cuboid

Topic 7: Volume

Question 14

Find the volume triangular prism below

Answer = _________________

Question 15

Find the volume of the hexagonal prism below

Answer = _________________

Topic 7: Volume

Question 16

Find the surface area and volume of the sphere below.

Answer = ______________

Question 17

Find the volume of the triangular-based pyramid.

Answer = _______________

Topic 7: Volume

Question 18

Find the volume of the square-based pyramid.

Answer = _________________

Question 19

Find the surface area and volume of the sphere below

Surface area = ____________

Volume = ______________

Topic 7: Volume

Question 20

Find the volume and surface area of the cone below

Answer = _____________

Question 21

Find the volume and surface area of the cone below

Answer = _____________

Topic 7: Volume

Question 22

Calculate the volume cuboid that is 5 m long, 3 m wide and 2 m high.

Answer = _____________

Question 23

The box is 5cm long, 8cm wide and 2cm high. Calculate the surface area of this box.

Answer = ______________

Question 24

A book is 19 centimetres wide, 26 centimetres long and 2.5 centimetres thick. There are 8 books

placed on top of each other. What is the volume taken up by them?

Answer = ______________

Topic 7: Volume

Question 25

James has a cube-shaped pencil case with a lid. Given that the length of the pencil case is 5cm

a. Find the volume of the pencil case

Answer = ______________

b. Find the surface area of the pencil case

Answer = ______________

c. Find the surface of the pencil case when the lid is removed.

Answer = ______________

Topic 7: Volume

Question 26

A car’s petrol tank measures 50cm by 60cm by 20cm.

a.. How many litres of fuel can the petrol tank hold? Answer in millilitres (ml). Note that 1cm3 is

equal to 1ml

Answer = ______________

b.. If the tank can be filled at a rate of 2000 ml per second, how many seconds will it take to fill the

tank?

Answer = ______________

c. The rate at which the tank is being filled has been reduced to 500ml per seconds. How many

minutes will it take to fill the tank.

Answer = ______________

Topic 7: Volume

Question 27

A container measures 20cm by 15cm by 5cm.

(a) It is one quarter full of water. How much water is in the container? Answer in millilitres.

Answer = ______________

(b) If it is leaking at a rate of 25 millilitres per second, how long will it take to empty the container?

Answer = ______________

(c) What is the maximum capacity of the container (when filled with water)?

Answer = ______________

Topic 7: Volume

Question 28

A swimming pool is 8m long, 6m wide and 1.5m deep. The water-resistant paint needed for the pool

costs £6 per square meter.

1. How much will it cost to paint the interior surfaces of the pool?

Answer = ______________

2. How many litres of water will be needed to fill it? Note that 1m3 is equal to 1000 litres

Answer = ______________

Topic 7: Volume

Question 29

Find the volume of the shape below

Answer = ______________

Topic 7: Volume

Question 30

The top third of the cone has been cut away. The resulting frustum has a base radius of 8m.

Calculate the volume of the frustum.

Answer = _______________

Question 31

Find the total surface area of the solid prism shown in the diagram. The cross section is an isosceles

trapezium

Answer = _______________

5 cm

3 cm

4 cm

9 cm

8 cm

Topic 7: Volume

Question 32

Find the surface area of the hemisphere below

Answer = ___________

Question 33

A solid object is formed by joining a hemisphere to a cylinder.

Both the hemisphere and the cylinder have a diameter of 4.2 cm.

The cylinder has a height of 5.6 cm.

Calculate the total surface area of the whole object.

Give your answer to 3 SF.

Answer = ____________

5.5 cm

4.2 cm

5.6 cm

Topic 7: Volume