Test your hypothesis with the applet below. Click the button to pour the water from the cone to the cylinder. Then, refill the water in the cone and repeat until the cylinder is full.

How many cones of water did it take to fill the cylinder?
What fraction of the cylinder does one cone fill?
Recall that the volume of a cylinder can be found using the formula V =\pi r^2 h. Using formula for the volume of a cylinder and your answers to the questions above, develop the equation for the volume of a cone.

Loading interactive...

Notice that if a cone and a cylinder have equal radius and height, the cone will fill the cylinder exactly three times. This means that the volume of a cone is \dfrac{1}{3}\,the volume of the cylinder.

Volume of a cone

V=\dfrac{1}{3}\pi r^2h where r is the radius and h is the height of the cone.

Examples

Example 1

Find the volume of the cone shown. Round your answer to two decimal places.

A cone with radius of 2 meters and height of 6 meters. Ask you teacher for more information

Worked Solution

Create a strategy

Use the formula of the volume of cone.

Apply the idea

We have been given values for radius r=2 and height h=6.

\displaystyle V	\displaystyle =	\displaystyle \frac{1}{3}\pi r^2h	Use the formula
	\displaystyle =	\displaystyle \frac{1}{3}\times\pi \times 2^2\times 6	Substitute r = 2 and h = 6
	\displaystyle =	\displaystyle 25.13\, \text{cm}^3	Evaluate

Idea summary

The volume, V , of a cone can be calculated using the formula V=\frac{1}{3}\pi r^2h

where r is the radius and h is the height of the cone.

Outcomes

8.G.C.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

10.02 Volume of cones

Introduction

Ideas

Volume of cones

Exploration

Examples

Example 1

Outcomes

8.G.C.9

What is Mathspace

About Mathspace