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The surface area of a sphere

I can calculate the surface area of a sphere.

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Lesson 9 of 18

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Year 11

The surface area of a sphere

I can calculate the surface area of a sphere.

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Lesson details

Key learning points

There is a formula for the surface area of a sphere.
Demonstration allows you to see that this formula works.
The formula can be used to calculate a missing measurement when the surface area is known.

Keywords

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

Common misconception

Pupils may forget the constant '4' when calculating the surface area.

Show the demonstration of the formula of the surface area using a different spherical fruit to see that it is always 4 regardless of the size of the sphere. You can also relate it to the 1/2 in the formula of the area of triangle.

You may wish to have pupils demonstrate the formula of the surface area of a sphere themselves before the lesson.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Match each letter to the name of the shape.

Correct Answer:A,Pyramid

Correct Answer:B,Cylinder

Correct Answer:C,Cone

Correct Answer:D,Cuboid

Q2.
Which calculation gives the surface area of a cylinder of radius 2 cm and height 9 cm?

Surface area = $$2 \pi \times 2 + \pi \times 2 \times 9^2$$

Surface area = $$ \pi \times 2^2 + 2\pi \times 2 \times 9$$

Correct answer: Surface area = $$2 \pi \times 2^2 + 2\pi \times 2 \times 9$$

Surface area = $$ 2\pi \times 2 \times 9$$

Surface area = $$\pi \times 2^2 + 2\pi \times 2^2 \times 9$$

Q3.
The area of a circle is 19.6 cm². What is the radius of the circle? Give your answer correct to 1 decimal place.

1.4 cm

Correct answer: 2.5 cm

4.4 cm

5.0 cm

Q4.
A cylinder has a radius of 3 mm and a height of 10 mm. The volume of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm³.

Correct Answer: 90

Q5.
A cylinder has a radius of 3 mm and a height of 10 mm. The surface area of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm².

Correct Answer: 78

Q6.
The volume of a cube is 125 cm³. The surface area of the cube is cm².

Correct Answer: 150

Assessment exit quiz

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6 Questions

Q1.
Which of these 3D shapes is a sphere?

Correct Answer: An image in a quiz

Q2.
Complete the formula for the surface area of a sphere, with a radius of $$r$$: surface area = $$\pi r^2$$.

Correct Answer: 4

Q3.
Match each sphere to its surface area.

Correct Answer:Radius of sphere = 6 cm,144𝜋

Correct Answer:Diameter of sphere = 8 cm,64𝜋

Correct Answer:Diameter of sphere = 0.5 cm,0.25𝜋

Correct Answer:Radius of sphere = 0.5 cm,𝜋

Correct Answer:Diameter of sphere = 4 cm,16𝜋

Correct Answer:Radius of sphere = 1 cm,4𝜋

Q4.
A sphere has a surface area of 196𝜋 m². The radius of the sphere is m.

Correct Answer: 7

Q5.
The radius of this hemisphere is 6 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

226 cm²

Correct answer: 339 cm²

452 cm²

565 cm²

Q6.
The total surface area of this hemisphere is 192𝜋 cm². The radius of the hemisphere is cm.

Correct Answer: 8, 8 cm, 8cm

Lesson appears in

UnitMaths / 2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Maths

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The surface area of a sphere

The surface area of a sphere

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Match each letter to the name of the shape.

Q2.Which calculation gives the surface area of a cylinder of radius 2 cm and height 9 cm?

Q3.The area of a circle is 19.6 cm². What is the radius of the circle? Give your answer correct to 1 decimal place.

Q4.A cylinder has a radius of 3 mm and a height of 10 mm. The volume of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm³.

Q5.A cylinder has a radius of 3 mm and a height of 10 mm. The surface area of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm².

Q6.The volume of a cube is 125 cm³. The surface area of the cube is cm².

Assessment exit quiz

6 Questions

Q1.Which of these 3D shapes is a sphere?

Q2.Complete the formula for the surface area of a sphere, with a radius of $$r$$: surface area = $$\pi r^2$$.

Q3.Match each sphere to its surface area.

Q4.A sphere has a surface area of 196𝜋 m². The radius of the sphere is m.

Q5.The radius of this hemisphere is 6 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

Q6.The total surface area of this hemisphere is 192𝜋 cm². The radius of the hemisphere is cm.

Lesson appears in

UnitMaths / 2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Maths

Q1.
Match each letter to the name of the shape.

Q2.
Which calculation gives the surface area of a cylinder of radius 2 cm and height 9 cm?

Q3.
The area of a circle is 19.6 cm². What is the radius of the circle? Give your answer correct to 1 decimal place.

Q4.
A cylinder has a radius of 3 mm and a height of 10 mm. The volume of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm³.

Q5.
A cylinder has a radius of 3 mm and a height of 10 mm. The surface area of the cylinder, in terms of $$\pi$$, is $$\pi $$ mm².

Q6.
The volume of a cube is 125 cm³. The surface area of the cube is cm².

Q1.
Which of these 3D shapes is a sphere?

Q2.
Complete the formula for the surface area of a sphere, with a radius of $$r$$: surface area = $$\pi r^2$$.

Q3.
Match each sphere to its surface area.

Q4.
A sphere has a surface area of 196𝜋 m². The radius of the sphere is m.

Q5.
The radius of this hemisphere is 6 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

Q6.
The total surface area of this hemisphere is 192𝜋 cm². The radius of the hemisphere is cm.