Checking and securing understanding of surface area of a cylinder | Maths

Starter quiz

A ______ is a 3D shape with a base that is a circle and a parallel opposite face that is identical.

'cylinder' ✓
The formula for the volume of a cylinder is __________.

$V= r^2 h$

$V=\pi r h + \pi r^2$

$V=2\pi r^2 h$

$V=\pi r^2 h$ ✓

$V= \pi r h$
Which of these are correct for the volume, $V$ , of this cylinder?

$V=1440\pi$ ✓

$V=\pi\times 144 \times 10$ ✓

$V=\pi\times 12 \times 10^2$

$V=\pi\times 12^2 \times 10$ ✓

$V=\pi\times 12 \times 10$
Calculate the volume of this semi-cylinder. Give your answer correct to 3 significant figures.

3390 mm³

1700 mm³

848 mm³ ✓

565 mm³

424 mm³
A cylinder fits perfectly inside a cube. The volume of the cube is 512 cm³. The volume of the cylinder in terms of π is ______π cm³.

'128' ✓
The volume of this cylinder is 405π cm³ . The radius of the cylinder is ______ cm.

'9' ✓

Exit quiz

The curved surface of a cylinder can be flattened out to form a 2D shape which is a ______.

'rectangle' ✓
A cylindrical tube is cut and unfolded into a rectangle. Find the values of $a$ and $b$ on the lengths of the rectangle.

$a=6$

$a=20$ ✓

$b=12$

$b=6 \pi$

$b=12 \pi$ ✓
Which formula gives the surface area of a cylinder of radius $r$ and height $h$ ?

Surface area = $2 \pi r + \pi r h^2$

Surface area = $\pi r^2 + 2\pi r h$

Surface area = $\pi r^2 + 2\pi r^2 h$

Surface area = $2 \pi r^2 + 2\pi r h$ ✓

Surface area = $2\pi r h$
Find the surface area of a cylinder with radius 5 cm and height 8 cm. Give your answer correct to 3 significant figures.

157 cm²

204 cm²

251 cm²

408 cm² ✓
A cylinder has a radius of 4 mm and a height of 12 mm. The surface area of the cylinder, in terms of $\pi$ , is ______ $\pi$ mm².

'128' ✓
The surface area of this cylinder is 276π cm². The length of marked $x$ is ______ cm.

'17' ✓

Worksheet

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Lesson Details

Key learning points

Drawing the net of a cylinder helps deduce the formula for the surface area.
The formula can be used to find the surface area of any cylinder.
Unknown lengths can be found when the surface area is known.

Common misconception

Pupils can make errors if given the dimensions/measurements of the cylinder using different units (for example the radius is given in cm and the length in m).

Remind pupils to convert all measurements to the same unit (such as cm or m) before starting the calculation. Usually there is a prompt in the question to use as a guide, for example give your answer in square centimetres.

Keywords

Cylinder - A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.
Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.