## 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.

- 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.
- Good luck!

## How to Find the Volume of a Cylinder

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

## Step-by-Step:

# 1

Start with the formula:

Volume = πr^{2}h

**Don't forget:** π is

pi (≈ 3.14)

**and** r

^{2} = r × r (r

squared).

# 2

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

Volume = π × 5^{2} × 10
Volume = π × 5 × 5 × 10
Volume = π × 250
Volume = 3.14 × 250
Volume = 785 cm^{3}

## Answer:

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

^{3}.

## 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?