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.

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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
The diagram shows a solid hemisphere.Surface area of sphere $= 4\pi r^2$

The total surface area of the hemisphere is $60\pi$ cm²

Find the diameter of the hemisphere.

Give your answer in the form $a\sqrt{b}$ , where $a$ and $b$ are integers and $b$ is prime.

(4 marks)
Level 5 · 4 marksTry it
2
The diagram shows a solid frustum.Curved surface area of cone $= \pi r l$

The top of the frustum is a circle of radius $4$ cm.

The base of the frustum is a circle of radius $6$ cm.

The slant height of the frustum is $5$ cm.

Calculate the total surface area of the frustum.

Give your answer correct to $3$ significant figures.

(5 marks)
Level 5 · 5 marksTry it
3
The diagram shows a storage tank made from a cylinder with a hemisphere on top. The cylinder has radius $3$ m and height $5$ m.Diagram NOT accurately drawn

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

The outside of the tank, not including its base, is going to be painted. One tin of paint covers $12$ m² and costs £8.99.

Work out the total cost of the paint needed. You must show all your working.
Level 5 · 5 marksTry it
4
A rocket-shaped solid is made from a cylinder with a cone fixed on top.

The cylinder has radius $2$ cm and height $7$ cm. The cone has radius $2$ cm and slant height $5$ cm.

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

Work out the total surface area of the solid. Give your answer in terms of $\pi$ .
Level 5 · 4 marksTry it