GCSE · Perimeter, area & volume

Surface area of prisms, cylinders, cones & spheresExam-style questions

Surface area as the area of the unfolded net — counting a prism's faces without missing any, why a cylinder's curved surface is 2πrh, cones and the slant height, spheres, and the hemisphere trap.

Start practising Read the lesson

17 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 closed cylindrical water tank has radius $1.2$ m and height $2.5$ m.

The whole outside surface of the tank, including the top and bottom, is to be painted.

One litre of paint covers $12$ m $^2$ . Paint is sold in $1$ -litre tins costing £ $8.50$ each.

Work out the cost of the paint. You must show your working. [5]
Level 4 · 5 marksTry it
2
The diagram shows a cone with radius $9$ cm and perpendicular height $12$ cm.Diagram NOT accurately drawn

Curved surface area of a cone $= \pi r l$

Work out the total surface area of the cone. Give your answer in terms of $\pi$ .
Level 4 · 4 marksTry it
3
The diagram shows a solid hemisphere with radius $5$ cm.Diagram NOT accurately drawn

Surface area of a sphere $= 4\pi r^2$

Work out the total surface area of the hemisphere. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
4
An open-topped cylindrical tank has radius $3$ m and height $10$ m.

Work out the total surface area of the tank (the base and the curved surface, with no top).

Give your answer correct to 3 significant figures.
Level 4 · 3 marksTry it
5
A sphere has radius $6$ cm.

Surface area of a sphere $= 4\pi r^2$

Work out the surface area of the sphere. Give your answer correct to 3 significant figures.
Level 4 · 2 marksTry it