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Level 5-6 Shapes - Volume and Capacity

Volume and capacity compare how much space shapes hold. Use cubes, prisms and cylinders to model real containers and calculate efficiently.

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Fascinating Fact:

The formula for a pyramid’s volume is (1/3) × base area × height. A square-based pyramid with base 6 cm and height 9 cm has volume (1/3) × 36 × 9 = 108 cm³.

In KS3 Maths, you calculate the volume of prisms and pyramids and connect capacity to real containers. You’ll apply formulas, convert between cm³, mL and L, and check that answers are sensible for everyday objects.

Key Terms

Volume: The amount of 3D space a solid occupies, measured in cubic units (e.g., cm³, m³).
Capacity: How much a container can hold, often measured in millilitres (mL) or litres (L).
Prism: A solid with identical parallel ends (bases) and rectangular side faces; volume = area of base × height.

Frequently Asked Questions (Click to see answers)

How do you find the volume of a cuboid in KS3?

Multiply its three dimensions: V = length × width × height. Keep units consistent and give the answer in cubic units such as cm³.

What’s the difference between volume and capacity?

Volume measures the space a solid takes up in cubic units. Capacity measures how much fluid a container holds in mL or L. For water, 1 cm³ equals 1 mL.

How do I calculate the volume of a pyramid?

Use V = (area of base × height) ⁄ 3. Find the base area first, then multiply by the perpendicular height and divide by 3.

Try These Related Quizzes

1 .

The volume of a cylinder is calculated using .......

π r² x length

π r³ x length

r² x length

r³ x length

Work out the are of the circle on a cylinder using ? r² then times by the length of the cylinder

2 .

An empty box can hold 100 smaller boxes each measuring 10 cm x 10 cm x 10 cm. How many litres of capacity does the empty box have?

10 litres

100 litres

500 litres

1,000 litres

1 litre = 1,000 cm³. Each of the smaller boxes has a volume of 1 litre

3 .

The volume of a cube is 125 cm³. What is the length of each edge of the cube?

2.5 cm

5 cm

12.5 cm

25 cm

The cube root of 125 = 5 because 5 x 5 x 5 = 125

4 .

A cuboid has a length of 10 cm, a width of 5 cm and a height of 15 cm. What is its volume?

250 cm³

500 cm³

750 cm³

1,000 cm³

750cm³ = 10 cm x 5 cm x 15 cm (V = l x w x h)

5 .

A cuboid has a volume of 72 cm³. Its length is 6 cm and its width is 4 cm. What is the height of the cuboid?

3 cm

4 cm

6 cm

7 cm

72 cm = 6 cm x 4 cm x 3 cm (V = l x w x h)

6 .

The volume of a cuboid is calculated using .......

length + width + height

length x width x height

length x width²

length x width³

V = l x w x h (V = lwh)

7 .

A tank has a length of 50 cm, a width of 60 cm and a height of 80 cm. How many litres of water can it hold?

120 litres

180 litres

240 litres

300 litres

50 cm x 60 cm x 80 cm = 240,000 cm³. Then divide by 1,000 as 1 litre = 1,000 cm³

8 .

What is the volume of a cuboid with a length of 8 cm, a width of 4 cm and a height of 6 cm?

180 cm³

18 cm³

192 cm³

219 cm³

8 x 4 x 6 = 192

9 .

Two cuboids have the same volume. The first measures 10 cm x 3 cm x 4 cm. The second measures 5 cm x 4 cm x what?

2 cm

4 cm

6 cm

8 cm

10 x 3 x 4 = 120 so 5 x 4 x ? = 120
5 x 4 = 20 so 20 x ? = 120
120 ÷ 20 = 6

10 .

An oil drum (cylinder) measures 88 cm tall and has a diameter of 60 cm. Approximately how many litres can it hold?

49 litres

149 litres

199 litres

249 litres

60 cm diameter = 30 cm radius. 30² = 900. 900 x 3.142 (?) = 2,827.8 Multiply this by 88 (height or length) = 248,846 cm³ or approximately 249 litres

You can find more about this topic by visiting BBC Bitesize - Volume

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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