# 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).

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)

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

catman3000 6 years ago from England, UK Author

Thanks. I used FX Draw 3.

pemekwulu 6 years ago from USA

Beautiful! What software did you use in drawing the cone?

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