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Checking and securing understanding of volume of a cylinder

I can calculate the volume of a cylinder.

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Lesson 5 of 18

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Year 11

Checking and securing understanding of volume of a cylinder

I can calculate the volume of a cylinder.

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Key learning points

A cylinder is not a prism but has a similar structure.
The formula for the volume of a cylinder can be derived by using the formula for a prism.
This can be used to find the volume of any cylinder.
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.

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.

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

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.

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?

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.

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.

Correct Answer: 207

Assessment exit quiz

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6 Questions

Q1.
Which of these shapes is a cylinder?

Correct Answer: 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?

$$V=\pi\times 10 \times 8$$

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.

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.

Correct Answer: 432

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

Correct Answer: 6

Lesson appears in

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

Maths

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Checking and securing understanding of volume of a cylinder

Checking and securing understanding of volume of a cylinder

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.This prism has two congruent regular octagonal faces and congruent rectangular faces.

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

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

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?

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.

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.

Assessment exit quiz

6 Questions

Q1.Which of these shapes is a cylinder?

Q2.Which of these is the formula for the volume of a cylinder?

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

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

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.

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

Lesson appears in

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

Maths

Q1.
This prism has two congruent regular octagonal faces and congruent rectangular faces.

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

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

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?

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.

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.

Q1.
Which of these shapes is a cylinder?

Q2.
Which of these is the formula for the volume of a cylinder?

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

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

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.

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