GCSE · Perimeter, area & volume

Volume of prisms, cylinders, cones & spheresExam-style questions

Why a prism's volume is cross-section × length, why a cylinder is just a circular prism, where the ⅓ in pyramid and cone formulas fits in, spheres and hemispheres, and litres.

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19 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A solid hemisphere has radius $4.5$ cm.

Volume of a sphere $= \dfrac43\pi r^3 \qquad$ Surface area of a sphere $= 4\pi r^2$

(a) Work out the volume of the hemisphere. Give your answer correct to 3 significant figures. (2 marks)

(b) Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures. (2 marks)
Level 3 · 4 marksTry it
2
A solid cone has base radius $6$ cm and slant height $10$ cm.Diagram NOT accurately drawn

Volume of a cone $= \dfrac{1}{3}\pi r^2 h$

Work out the volume of the cone.

Give your answer correct to 3 significant figures. (4 marks)
Level 3 · 4 marksTry it
3
The diagram shows a prism whose cross-section is a trapezium. The parallel sides of the trapezium are $6$ cm and $10$ cm and the perpendicular distance between them is $4$ cm. The prism is $11$ cm long.Diagram NOT accurately drawn

Work out the volume of the prism.
Level 3 · 3 marksTry it
4
A cylindrical water tank has diameter $60$ cm and height $70$ cm.

Work out the volume of the tank in litres. Give your answer correct to the nearest litre. ( $1$ litre $= 1000$ cm³.)
Level 3 · 3 marksTry it
5
A cuboid-shaped fish tank measures $40$ cm by $25$ cm by $30$ cm.

$1$ litre $= 1000$ cm³

Work out the capacity of the tank in litres.
Level 3 · 2 marksTry it