The volume of a sphere | Maths | Quizalize & Oak National Academy

Starter quiz

A ______ is a 3D shape, where every point on its surface is equidistant from the centre.

'sphere' ✓
Which of the following calculates the surface area of a sphere, with a radius of $r$ ?

$4 \pi r$

$4 \pi r^2$ ✓

$4 \pi r^3$

$2\pi r^2$

$2\pi r^3$
Match each sphere to its surface area.

Diameter of sphere = 10 cm

⇔

100𝜋 ✓

Radius of sphere = 4 cm

⇔

64𝜋 ✓

Radius of sphere = 3 cm

⇔

36𝜋 ✓

Diameter of sphere = 1 cm

⇔

𝜋 ✓

Radius of sphere = 2 cm

⇔

16𝜋 ✓

Diameter of sphere = 2 cm

⇔

4𝜋 ✓
A sphere has a surface area of 9𝜋 m². The radius of the sphere is ______ m.

'1.5' ✓
The radius of this hemisphere is 20 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

1260 cm²

2510 cm²

3770 cm² ✓

5030 cm²
The total surface area of this hemisphere is 432𝜋 cm². The radius of the hemisphere is ______ cm.

'12' ✓

A sphere is a 3D shape, where every point on its surface is ______ from the centre.

'equidistant' ✓
Work out the volume of a sphere with radius 2.5 m. Give your answer correct to 1 decimal place.

19.6 m³

20.8 m³

26.2 m³

49.1 m³

65.4 m³ ✓
A sphere has a radius of 6 mm. The volume of the sphere, in terms of 𝜋, is ______𝜋 mm³.

'288' ✓
Which of these calculations finds the volume of a hemisphere with a radius of 12 cm?

$\frac{2}{3} \times \pi \times 12^3$ ✓

$\frac{2}{6} \times \pi \times 12^3$

$\frac{4}{3} \times \pi \times 6^3 \div 2$

$\frac{1}{2} \times \frac{4}{3} \times \pi \times 12^3$ ✓

$\frac{4}{3} \times \pi \times 8^3 \div 2$
The volume of a hemisphere with a radius of 12 cm, in terms of $\pi$ , is ______ $\pi$ cm³.

'1152' ✓
The volume of a hemisphere is 144𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is ______𝜋 cm².

'108' ✓

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The volume of a sphere can be found by displacement.
Putting a sphere into a cylinder filled with water displaces the water.
When the sphere is removed, the water level drops.
The volume of the sphere is the difference between the volume of the cylinder and water.
There is a formula you can use to calculate the volume of a sphere.

Pupils may multiply the radius of the sphere by the constant before cubing it.

Remind pupils of the order of operations and the need to cube the radius before multiplying by the constants in the formula.

Sphere - A sphere is a 3D shape, where every point on its surface is equidistant from the centre.