Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 8

Volume of cylinders

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

Download all resources
Share activities with pupils
New
New
Year 8

Volume of cylinders

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

Download all resources
Share activities with pupils

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.

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.

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.

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

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

Skip video

Loading...

Starter quiz

Download starter quiz

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

Download exit quiz

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.