Volume of prisms

The Maths Habit

How many litres of water are
in an Olympic swimming pool?

About 2 500 000

Volume
The space inside a 3D shape.
Prism
A 3D shape that is the same all the way through.
Cross-section
The face you see when you slice through a prism.

Volume = area of cross-section × length

The cross-section has an area of 20 cm2.
The prism is 7 cm long. What is its volume?

140 cm3

Work out the volume.

Work out the volume.

V = area of cross-section × length
cross-section = ½ × 9 × 4 = 18 cm2
V = 18 × 12 = 216 cm3
Answer216 cm3
V = area of cross-section × length
cross-section = ½ × 7 × 8 = 28 cm2
V = 28 × 5 = 140 cm3
Answer140 cm3
V = area of cross-section × length
cross-section = ½ × 9 × 4 = 18 cm2
V = 18 × 12 = 216 cm3
Answer216 cm3
V = area of cross-section × length
cross-section = ½ × 12 × 5 = 30 cm2
V = 30 × 6 = 180 cm3
Answer180 cm3
V = area of cross-section × length
cross-section = ½ × 9 × 4 = 18 cm2
V = 18 × 12 = 216 cm3
Answer216 cm3
V = area of cross-section × length
cross-section = ½ × 10 × 7 = 35 cm2
V = 35 × 8 = 280 cm3
Answer280 cm3
V = area of cross-section × length
cross-section = ½ × 9 × 4 = 18 cm2
V = 18 × 12 = 216 cm3
Answer216 cm3
V = area of cross-section × length
cross-section = ½ × 6 × 5 = 15 cm2
V = 15 × 3.5 = 52.5 cm3
Answer52.5 cm3
V = area of cross-section × length
cross-section = ½ × 9 × 4 = 18 cm2
V = 18 × 12 = 216 cm3
Answer216 cm3
V = area of cross-section × length
cross-section = ½ × 4 × 3 = 6 m2
V = 6 × 9 = 54 m3
Answer54 m3

Volume of prisms worksheet, page 1

Volume of prisms worksheet, page 2

Answer sheet

  1. The cross-section of a prism is a trapezium. Its parallel sides are 4 cm and 10 cm, and they are 5 cm apart. The prism is 6 cm long. Work out its volume.

    210 cm3

  2. A triangular prism has a volume of 300 cm3. Its cross-section has an area of 25 cm2. How long is the prism?

    12 cm

An Olympic pool is 50 m long,
25 m wide and 2 m deep.
1 m3 holds 1000 litres.
How many litres does it hold?

2 500 000 litres

  1. Work out the volume of the cuboid.

    120 cm3
    6 cm4 cm5 cm

  2. Work out the volume of the triangular prism.

    168 cm3
    8 cm6 cm7 cm

  3. The volume of this prism is 96 cm³. Find its length, l.

    l = 8 cm
    4 cm6 cml
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