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      Checking and securing understanding of volume of a cylinder

      Lesson details

      Learning outcome

      I can calculate the volume of a cylinder.

      Key learning points

      1. A cylinder is not a prism but has a similar structure.
      2. The formula for the volume of a cylinder can be derived by using the formula for a prism.
      3. This can be used to find the volume of any cylinder.
      4. Unknown lengths can be found when the volume of a cylinder 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.

      • Volume - Volume is the amount of space occupied by a closed 3D shape.

      Common misconception

      When questions are in context, the height of the cylinder may be described as the depth or length and this can cause some pupils to struggle if they have learned a formula with a particular word.

      Remind pupils that the volume of a 3D shape comes from the area of a cross section multiplied by the height or depth. Discuss which length this would be, using a diagram to support.

      Teacher tip

      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.

      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.
      This prism has two congruent regular octagonal faces and congruent rectangular faces.

      An image in a quiz
      Correct Answer: eight, 8

      Q2.
      Izzy takes some measurements from a cube. Match each measurement to its correct value.

      Correct Answer:Area of cross-section,25 cm²
      Correct Answer:Length of one side,5 cm
      Correct Answer:Perimeter of cross-section,20 cm
      Correct Answer:Surface area,150 cm²
      Correct Answer:Volume,125 cm³

      Q3.
      The surface area of this octagonal prism is cm².

      An image in a quiz
      Correct Answer: 668

      Q4.
      The diagram shows a prism unfolded into its net. The perimeter of the cross-sectional face is 70 cm. Which of these statements are correct?

      An image in a quiz
      Dimensions of rectangle in the net: 6 cm by 320 cm
      Correct answer: Dimensions of rectangle in the net: 6 cm by 70 cm
      Total surface area = (320 + 5 × 70) cm²
      Correct answer: Total surface area = (2 × 320 + 70 × 6) cm²
      Total surface area = (2 × 320 + 5 × (70 × 6)) cm²

      Q5.
      The diagram shows the net of a triangular prism. The depth of the prism is 4 cm. The surface area of the prism that can be formed from this net is cm².

      An image in a quiz
      Correct Answer: 144

      Q6.
      The cross-section of this prism is an equilateral triangle. The surface area of this triangular prism is cm². Give your answer correct to 3 significant figures.

      An image in a quiz
      Correct Answer: 207

      6 Questions

      Q1.
      Which of these shapes is a cylinder?

      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.
      Which of these is the formula for the volume of a cylinder?

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

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

      An image in a quiz
      $$V=\pi\times 10 \times 8$$
      Correct answer: $$V=\pi\times 10^2 \times 8$$
      $$V=\pi\times 10 \times 8^2$$
      Correct answer: $$V=\pi\times 100 \times 8$$
      Correct answer: $$V=800\pi$$

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

      An image in a quiz
      1884 cm³
      1130 cm³
      Correct answer: 565 cm³
      283 cm³
      180 cm³

      Q5.
      A cylinder fits perfectly inside a cube. The volume of the cube is 1728 cm³. The volume of the cylinder in terms of π is π cm³.

      An image in a quiz
      Correct Answer: 432

      Q6.
      The volume of this cylinder is 360π cm³ . The radius of the cylinder is cm.

      An image in a quiz
      Correct Answer: 6

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