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 wooden block is in the shape of a cuboid.

The block is $12$ cm long.

The width of the block is $3$ cm more than its height.

The volume of the block is $336$ cm³

Work out the total surface area of the block.

You must show all your working.

(5 marks)
Level 5 · 5 marksTry it
2
A solid cone has base radius $12$ cm and perpendicular height $20$ cm.

The top of the cone is cut off by a cut parallel to the base, removing a smaller cone of perpendicular height $5$ cm. The solid that is left is called a frustum.Diagram NOT accurately drawn

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

Work out the volume of the frustum. Give your answer in terms of $\pi$ .
Level 5 · 4 marksTry it
3
A solid metal cylinder has radius $6$ cm and height $10$ cm.

The cylinder is melted down and recast into solid spheres of radius $3$ cm.

Volume of a sphere $= \dfrac{4}{3}\pi r^3$

Work out how many complete spheres can be made.
Level 5 · 4 marksTry it