GCSE Maths revision · Geometry and measures

Volume and surface area of prisms

Foundation and Higher

The idea

Volume of a prism $=$ area of the cross-section $\times$ length. A cylinder is a prism with a circular cross-section: $V = \pi r^2 h$ . Surface area is the total area of every face.

Find the area of the cross-section.
Multiply by the length for the volume (cubic units).
For surface area, add the area of each face (square units): a cylinder is $2\pi r^2 + 2\pi rh$ .

Watch out Volume is in cubic units and surface area in square units: do not mix them up.

See it worked

Worked exampleNon-calculator3 marks

This question is about volumes of prisms.

(a) A prism has a cross-section of area $12\text{ cm}^2$ and a length of 9 cm. Work out its volume.

(b) A cuboid measures 5 cm by 4 cm by 3 cm. Work out its volume.

(a) Volume of a prism $=$ area of cross-section $\times$ length $= 12 \times 9 = 108$ .
(b) $5 \times 4 \times 3 = 60$ .

Answer (a) $108\text{ cm}^3$ ; (b) $60\text{ cm}^3$

Your turn

Question 1Non-calculator3 marks

A prism has a right-angled triangle as its cross-section. The triangle's sides are 3 cm, 4 cm and 5 cm (the right angle is between the 3 cm and 4 cm sides). The prism is 10 cm long.

Work out the total surface area of the prism.

Question 2Non-calculator4 marks

A closed cylinder has radius 3 cm and height 8 cm.

(a) Find its volume exactly in terms of pi.

(b) Find the total surface area exactly.

Question 3Calculator allowed4 marks

A closed cylinder has radius 5 cm and volume $1000\text{ cm}^3$ .

Work out the total surface area of the cylinder. Give your answer correct to 3 significant figures.

In past papers

122 official questions in 106 papers since 2017. The latest:

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