Calculate the Volume of a Cone

The formula for the volume of a cone, V, in terms of its base radius, r, is:

This is similar to the formula for the volume of a cylinder, but remember to divide by 3.

Example

Calculate the volume of the cone shown below in cm³ to 3 significant figures.

Answer

Diameter d = 8 cm

Radius r = 8 ÷ 2 = 4 cm

Height h = 10 cm

Volume = ¹/3πr²h 

(π x 4² x 10) ÷ 3 = 167.55.... ≈ 168 cm³ (3 s.f.)

It is important to get the order correct in these calculations!

Did you spot the brackets around most of the equation?

We need to do all the multiplication in the brackets before dividing by 3.

Let's try some questions now.