Mathematics-Monster.com
(#mm)

menu

Finding the Volume of a Cylinder
(KS3, Year 8)

homegeometryfinding the volume of a cylinder
The volume of a cylinder is found using the formula:

volume cylinder formula In this formula, r is the radius of the cylinder and h is the height of the cylinder. The image below shows what we mean by the radius and height:

cylinder radius height1

"Find the Volume" Widget

Here is a widget to help you learn the formulas for finding the volumes of different shapes.
  • Click on the shape you're learning about.
  • Click on the pad to start.
  • Follow the instructions in the bottom-left corner.
  • On the last click, the formula, workings, and answer will appear in the yellow box.
  • Enjoy!
full page

How to Find the Volume of a Cylinder

Question

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm, as shown below?
cylinder radius height

Step-by-Step:

1

Start with the formula:
Volume = πr2h
Don't forget: π is pi (≈ 3.14) and r2 = r × r (r squared).

2

Substitute the radius and the height into the formula. In our example, r = 5 and h = 10.

Volume = π × 52 × 10

Volume = π × 5 × 5 × 10

Volume = π × 250

Volume = 3.14 × 250

Volume = 785 cm3

Answer:

The volume of the cylinder with a radius of 5 cm and a height of 10 cm is 785 cm3.

Lesson Slides

The slider below shows another real example of how to find the volume of a cylinder.

What Is a Cylinder?

A cylinder has two ends that are circles that are parallel to each other and are joined by a curved surface.

A Sphere in a Cylinder

sphere in cylinder If a sphere is placed in a cylinder, the volume of the sphere is exactly two-thirds the volume of the cylinder. Can you work out why?

A Cone in a Cylinder

cone in cylinder If a cone is placed in a cylinder, the volume of the cone is exactly a third of the volume of the cylinder. Can you work out why?
author logo

This page was written by Stephen Clarke.

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.