# 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.

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