# Volumes of Cones. How to work out the volume of a cone using the height and radius.

To find the volume of a cone follow these 3 simple steps:3

**Step 1** First find
the area of the circle at the base of cone. Do this by using the formula **A = π × r².**

[π = Pi = 3.142 and r = radius of the circle (the distance halfway across)]

**Step 2** Multiply the
answer from step 1 by the perpendicular height of the cone (the perpendicular
height is the vertical height not the slanting height).

**Step 3** Finally,
divide your answer from step 2 by 3.

However, if you are confident with your algebra then you can use the formula:

**V = 1/3 × π × r² × h**

Let’s take a look at an example.

**Example 1 **

Find the volume of this cone:

First of all let’s use the 3 steps shown above and then we shall
use the formula **V = 1/3 × π × r² × h**

**Step 1** First find
the area of the circle at the base of cone. Do this by using the formula **A = π × r².**

A = π × r².

A = π × 3² (since the radius of the circle is 3cm)

A = 28. 3 cm² (rounded to 3 signifcant figures)

**Step 2** Multiply the
answer from step 1 by the perpendicular height of the cone (the perpendicular
height is the vertical height not the slanting height).

28.3 × 8 = 226.4 (since the perpendicular height of the cone is 8cm)

**Step 3** Finally,
divide your answer from step 2 by 3.

226.4 ÷ 3

= 74.5 cm³ (rounded to 3 significant figures)

Now let’s find the volume by substituting the height and radius directly into the formula.

The radius of the cone is 3cm and the perpendicular height is 8 cm

V = 1/3 × π × r² × h

V = 1/3 × π × 3² × 8

V = 75.4 cm³ (to 3 significant figures)

Notice that the last answer is a little more precise than the first answer.

## More by this Author

- 0
If you are asked to work out the product of two numbers then you need to multiply the two numbers together. If you are asked to find the sum of two numbers then you need to add the numbers together. Example 1 Work...

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...