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      Checking and securing understanding of surface area of a cylinder

      I can efficiently calculate the surface area of a cylinder.

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      Lesson 6 of 18
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      • Year 11

      Checking and securing understanding of surface area of a cylinder

      I can efficiently calculate the surface area of a cylinder.

      Lesson details

      Key learning points

      1. Drawing the net of a cylinder helps deduce the formula for the surface area.
      2. The formula can be used to find the surface area of any cylinder.
      3. Unknown lengths can be found when the surface area is known.

      Keywords

      • Cylinder - A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.

      • Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

      Common misconception

      Pupils can make errors if given the dimensions/measurements of the cylinder using different units (for example the radius is given in cm and the length in m).

      Remind pupils to convert all measurements to the same unit (such as cm or m) before starting the calculation. Usually there is a prompt in the question to use as a guide, for example give your answer in square centimetres.

      Encourage pupils to clearly label on diagrams and in their solutions, if they have been given the radius or diameter of the circular cross-section.
      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).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      A is a 3D shape with a base that is a circle and a parallel opposite face that is identical.

      Correct Answer: cylinder

      Q2.
      The formula for the volume of a cylinder is __________.

      $$V= r^2 h$$
      $$V=\pi r h + \pi r^2$$
      $$V=2\pi r^2 h$$
      Correct answer: $$V=\pi r^2 h$$
      $$V= \pi r h$$

      Q3.
      Which of these are correct for the volume, $$V$$, of this cylinder?

      An image in a quiz
      Correct answer: $$V=1440\pi$$
      Correct answer: $$V=\pi\times 144 \times 10$$
      $$V=\pi\times 12 \times 10^2$$
      Correct answer: $$V=\pi\times 12^2 \times 10$$
      $$V=\pi\times 12 \times 10$$

      Q4.
      Calculate the volume of this semi-cylinder. Give your answer correct to 3 significant figures.

      An image in a quiz
      3390 mm³
      1700 mm³
      Correct answer: 848 mm³
      565 mm³
      424 mm³

      Q5.
      A cylinder fits perfectly inside a cube. The volume of the cube is 512 cm³. The volume of the cylinder in terms of π is π cm³.

      An image in a quiz
      Correct Answer: 128

      Q6.
      The volume of this cylinder is 405π cm³ . The radius of the cylinder is cm.

      An image in a quiz
      Correct Answer: 9

      Assessment exit quiz

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      6 Questions

      Q1.
      The curved surface of a cylinder can be flattened out to form a 2D shape which is a .

      Correct Answer: rectangle

      Q2.
      A cylindrical tube is cut and unfolded into a rectangle. Find the values of $$a$$ and $$b$$ on the lengths of the rectangle.

      An image in a quiz
      $$a=6$$
      Correct answer: $$a=20$$
      $$b=12$$
      $$b=6 \pi$$
      Correct answer: $$b=12 \pi$$

      Q3.
      Which formula gives the surface area of a cylinder of radius $$r$$ and height $$h$$?

      Surface area = $$2 \pi r + \pi r h^2$$
      Surface area = $$ \pi r^2 + 2\pi r h$$
      Surface area = $$\pi r^2 + 2\pi r^2 h$$
      Correct answer: Surface area = $$2 \pi r^2 + 2\pi r h$$
      Surface area = $$ 2\pi r h$$

      Q4.
      Find the surface area of a cylinder with radius 5 cm and height 8 cm. Give your answer correct to 3 significant figures.

      157 cm²
      204 cm²
      251 cm²
      Correct answer: 408 cm²

      Q5.
      A cylinder has a radius of 4 mm and a height of 12 mm. The surface area of the cylinder, in terms of $$\pi$$, is $$\pi$$ mm².

      Correct Answer: 128

      Q6.
      The surface area of this cylinder is 276π cm². The length of marked $$x$$ is cm.

      An image in a quiz
      Correct Answer: 17

      Lesson appears in

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

      Maths

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