## The Lesson

The volume of a cylinder is found using the 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:

## "Find the Volume" Widget

Here is a widget to help you learn the formulas to find the volumes of different shapes.

## Question

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

# 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

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

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?