# Volume of a cone

*Welcome to cone geometry!*

Let's kick off with how to work out the volume of a cone.

## Definition of a cone

A three dimensional shape made up of a flat circular base and a
curved surface which tapers to a point called the apex.

*For simplicity, we'll consider a right circular cone - one which has its apex directly above the center of its circular base.*

## Definition of volume of a cone

The amount of three dimensional space the cone occupies.

## Volume of cone formula

**Cone volume = 1/3 x circular base area x perpendicular height**

If h = perpendicular height and given a cone's base is circular and the area of a circle is πr² (where π= pi and r = radius of circle), the formula becomes

where Vcone = volume of cone.

Example calculation

Use the above formula to calculate volume of cone with base radius (r) 3cm
and perpendicular height (h) 4cm (where cm = centimeters).

Vcone

= 1/3 x πr²h

= 1/3 x π x 3² x 4

= 37.7cm³ (cubic centimeters) to 1 d.p. (one decimal place)

*To square the radius r on your calculator use **x**²**. *The key stroke sequence for the above example is 1, divide sign (*÷*), 3, multiply sign (x), pi sign (*π), multiply sign (x), 3, **x**², multiply sign (x), 4, equals sign (=). 37.69911184 should be displayed which is 37.7 to 1 d.p. You may need to access** x**² and* *π* via a shift or 2nd function button.

## How about a cone with base radius (r) 6m and perpendicular height (h) 8m (where m = meters)?

Vcone

= 1/3 x πr²h

= 1/3 x π x 6² x 8

= 301.59m³ (cubic meters) to 2 d.p. (two decimal places)

*Enter on your calculator 1, **divide sign (÷), 3, multiply sign (x), pi sign (**π), 6,** **x**²**, multiply sign (x), 8, equals sign (=). *

## Have a go!

Work out the volumes for different size cones by varying the base radius (r) and perpendicular height (h) values.

Learn more here:

Surface area of a cone

Volume of a cylinder

Surface area of a cylinder

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Volume of a cone