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Year 11
Higher

The volume of a sphere

I can calculate the volume of a sphere.

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New
New
Year 11
Higher

The volume of a sphere

I can calculate the volume of a sphere.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

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

Keywords

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

Common misconception

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.

This topic could be linked to volume scale factors to increase the challenge.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A is a 3D shape, where every point on its surface is equidistant from the centre.
Correct Answer: sphere
Q2.
Which of the following calculates the surface area of a sphere, with a radius of $$r$$?
$$4 \pi r$$
Correct answer: $$4 \pi r^2$$
$$4 \pi r^3$$
$$2\pi r^2$$
$$2\pi r^3$$
Q3.
Match each sphere to its surface area.
Correct Answer:Diameter of sphere = 10 cm,100𝜋

100𝜋

Correct Answer:Radius of sphere = 4 cm,64𝜋

64𝜋

Correct Answer:Radius of sphere = 3 cm,36𝜋

36𝜋

Correct Answer:Diameter of sphere = 1 cm,𝜋

𝜋

Correct Answer:Radius of sphere = 2 cm,16𝜋

16𝜋

Correct Answer:Diameter of sphere = 2 cm,4𝜋

4𝜋

Q4.
A sphere has a surface area of 9𝜋 m². The radius of the sphere is m.
Correct Answer: 1.5, 3/2
Q5.
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.
An image in a quiz
1260 cm²
2510 cm²
Correct answer: 3770 cm²
5030 cm²
Q6.
The total surface area of this hemisphere is 432𝜋 cm². The radius of the hemisphere is cm.
An image in a quiz
Correct Answer: 12, 12 cm, 12cm

Exit quiz

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6 Questions

Q1.
A sphere is a 3D shape, where every point on its surface is from the centre.
Correct Answer: equidistant, equi-distant, equal distance
Q2.
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
Correct answer: 65.4 m³
Q3.
A sphere has a radius of 6 mm. The volume of the sphere, in terms of 𝜋, is 𝜋 mm³.
Correct Answer: 288
Q4.
Which of these calculations finds the volume of a hemisphere with a radius of 12 cm?
Correct answer: $$ \frac{2}{3} \times \pi \times 12^3 $$
$$ \frac{2}{6} \times \pi \times 12^3 $$
$$ \frac{4}{3} \times \pi \times 6^3 \div 2$$
Correct answer: $$ \frac{1}{2} \times \frac{4}{3} \times \pi \times 12^3$$
$$ \frac{4}{3} \times \pi \times 8^3 \div 2$$
Q5.
The volume of a hemisphere with a radius of 12 cm, in terms of $$\pi$$, is $$\pi$$ cm³.
Correct Answer: 1152
Q6.
The volume of a hemisphere is 144𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is 𝜋 cm².
An image in a quiz
Correct Answer: 108