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New
Year 11
Higher

The surface area of a sphere

I can calculate the surface area of a sphere.

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Share activities with pupils
New
New
Year 11
Higher

The surface area of a sphere

I can calculate the surface area of a sphere.

Download all resources
Share activities with pupils

Lesson details

Key learning points

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

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.

Keywords

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

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Match each letter to the name of the shape.
An image in a quiz
Correct Answer:A,Pyramid

Pyramid

Correct Answer:B,Cylinder

Cylinder

Correct Answer:C,Cone

Cone

Correct Answer:D,Cuboid

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

Exit quiz

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6 Questions

Q1.
Which of these 3D shapes is a sphere?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
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

144𝜋

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

64𝜋

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

0.25𝜋

Correct Answer:Radius of sphere = 0.5 cm,𝜋

𝜋

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

16𝜋

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

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.
An image in a quiz
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.
An image in a quiz
Correct Answer: 8, 8 cm, 8cm