Volume of cylinders | Maths | Quizalize & Oak National Academy

Starter quiz

The area of a circle with radius 6 cm is ______ $\pi\text{ cm}^2$ .

'36' ✓
A circle has an area of $49\pi \text{ cm}^2$ . Which of the following statements about the circle are true?

The diameter is 7 cm.

The circumference is 14 cm.

The radius (in centimetres) is the square root of 49. ✓

The circumference is $14\pi \text{ cm}$ . ✓
A cuboid with a width of 3 m, a length of 8 m and a height of 6 m has a volume of ______ cm³.

'144' ✓
A cylinder is a 3D shape with a base that is a ______ 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.

'circle' ✓
Which of these triangular prisms has a volume of 2250 cm³?
A cuboid has a volume of 90 cm³. Its length is 5 cm. What could the dimensions of the cross-section be?

3 cm by 5 cm

3 cm by 6 cm ✓

8 cm by 10 cm

18 cm by 1 cm ✓

50 cm by 9 cm

Volume is the amount of space occupied by a closed ______ shape.

'3D' ✓
Which of the following is the formula for the volume of a cylinder, where $r$ is the radius and $h$ is the height?

$\pi r^3h$

$\pi r^2 h$ ✓

$\pi rh^2$

$r^2h$
A cylinder with a radius of 6 cm and a height of 10 cm, has a volume of ______ $\pi \text{ cm}^3$ .

'360' ✓
If the radius of a cylinder was to stay the same but the height was to change, what would happen to the volume?

increase

decrease

stay the same

you cannot tell ✓
A cylinder has a radius of 9 cm and a volume of $810\pi\text{ cm}^3$ . What is the length of the cylinder?

$10\pi \text{ cm}$

$10\text{ cm}$ ✓

$90\pi \text{ cm}$

$90 \text{ cm}$
If you know the volume of a cylinder and its length, what other information can you work out?

The radius of the circular face. ✓

The area of the circular face. ✓

The mass of the cylinder.

The surface area of the cylinder. ✓

The colour of the cylinder.

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A cylinder is not a prism but has a similar structure.
The formula for the volume of a cylinder can be derived by using the formula for a prism.
This can be used to find the volume of any cylinder.
Unknown lengths can be found when the volume of a cylinder is known.

Pupils may multiply the length and radius before squaring.

Remind students of the order of operations and link to the volume of a prism formula: finding the area of the cross-section first.

Prism - a polyhedron with a base that is a polygon and a parallel opposite face that is identical joined by parallelograms.
Radius - any line segment that joins the centre of a circle to its circumference.
Cylinder - 3D shape with a base that is a circle and a parallel opposite face that is identical and uniform cross-section.