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Year 8

Volume of cylinders

I can use the constant cross-sectional area property of cylinders to determine their volume.

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New
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Year 8

Volume of cylinders

I can use the constant cross-sectional area property of cylinders to determine their volume.

Download all resources
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Share activities with pupils
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Lesson details

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

  • Prism - a polyhedron with a base that is a polygon and a parallel opposite face that is identical joined by parallelograms.

  • Radius - any line segment that joins the centre of a circle to its circumference.

  • Cylinder - 3D shape with a base that is a circle and a parallel opposite face that is identical and uniform cross-section.

Common misconception

Pupils may multiply the length and radius before squaring.

Remind students of the order of operations and link to the volume of a prism formula: finding the area of the cross-section first.


To help you plan your year 8 maths lesson on: Volume of cylinders, download all teaching resources for free and adapt to suit your pupils' needs...

Comparing volumes of physical cylindrical vessels using liquid can lead to surprising results. Have pupils predict the order, before revealing.
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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).

Lesson video

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Starter quiz

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6 Questions

Q1.
The area of a circle with radius 6 cm is $$\pi\text{ cm}^2$$.
Correct Answer: 36
Q2.
A circle has an area of $$49\pi \text{ cm}^2$$. Which of the following statements about the circle are true?
The diameter is 7 cm.
The circumference is 14 cm.
Correct answer: The radius (in centimetres) is the square root of 49.
Correct answer: The circumference is $$14\pi \text{ cm}$$.
Q3.
A cuboid with a width of 3 m, a length of 8 m and a height of 6 m has a volume of cm³.
Correct Answer: 144
Q4.
A cylinder is a 3D shape with a base that is a 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.
Correct Answer: circle
Q5.
Which of these triangular prisms has a volume of 2250 cm³?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q6.
A cuboid has a volume of 90 cm³. Its length is 5 cm. What could the dimensions of the cross-section be?
3 cm by 5 cm
Correct answer: 3 cm by 6 cm
8 cm by 10 cm
Correct answer: 18 cm by 1 cm
50 cm by 9 cm

Exit quiz

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6 Questions

Q1.
Volume is the amount of space occupied by a closed shape.
Correct Answer: 3D, three dimensional, three-dimension
Q2.
Which of the following is the formula for the volume of a cylinder, where $$r$$ is the radius and $$h$$ is the height?
$$\pi r^3h$$
Correct answer: $$\pi r^2 h$$
$$\pi rh^2$$
$$r^2h$$
Q3.
A cylinder with a radius of 6 cm and a height of 10 cm, has a volume of $$\pi \text{ cm}^3$$.
Correct Answer: 360
Q4.
If the radius of a cylinder was to stay the same but the height was to change, what would happen to the volume?
increase
decrease
stay the same
Correct answer: you cannot tell
Q5.
A cylinder has a radius of 9 cm and a volume of $$810\pi\text{ cm}^3$$. What is the length of the cylinder?
$$10\pi \text{ cm}$$
Correct answer: $$10\text{ cm}$$
$$90\pi \text{ cm}$$
$$90 \text{ cm}$$
Q6.
If you know the volume of a cylinder and its length, what other information can you work out?
Correct answer: The radius of the circular face.
Correct answer: The area of the circular face.
The mass of the cylinder.
Correct answer: The surface area of the cylinder.
The colour of the cylinder.