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      Lesson details

      Learning outcome

      I can calculate the surface area of a sphere.

      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.

      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.

      Teacher tip

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

      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).

      Lesson video

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      Prior knowledge starter quiz

      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

      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

      To help you plan your 11 maths lesson on: The surface area of a sphere, download all teaching resources for free and adapt to suit your pupils' needs...