To find the volume of a cone, you use the formula:

V=13πr2hV=\frac{1}{3}\pi r^2hV=31​πr2h

where:

• rrr is the radius of the circular base of the cone,
• hhh is the perpendicular height of the cone,
• π\pi π is approximately 3.14159.

This formula means the volume of a cone is one-third the volume of a cylinder with the same base radius and height.

Steps to find the volume:

1. Measure or identify the radius rrr of the cone’s base.
2. Measure or identify the height hhh of the cone (the perpendicular distance from the base to the tip).
3. Substitute these values into the formula V=13πr2hV=\frac{1}{3}\pi r^2hV=31​πr2h.
4. Calculate the value using a calculator.

Example:

If a cone has a radius of 5 cm and a height of 12 cm, its volume is:

V=13×π×52×12=13×π×25×12=314.16 cm3(to 2 decimal places)V=\frac{1}{3}\times \pi \times 5^2\times 12=\frac{1}{3}\times \pi \times 25\times 12=314.16\text{ cm}^3\quad (\text{to 2 decimal places})V=31​×π×52×12=31​×π×25×12=314.16 cm3(to 2 decimal places)

If you know the diameter ddd instead of the radius, use r=d2r=\frac{d}{2}r=2d​ in the formula.

Volume using slant height:

If you only know the slant height LLL and the radius rrr, you can find the height using Pythagoras’ theorem:

h=L2−r2h=\sqrt{L^2-r^2}h=L2−r2​

Then the volume formula becomes:

V=13πr2L2−r2V=\frac{1}{3}\pi r^2\sqrt{L^2-r^2}V=31​πr2L2−r2​

This allows you to calculate the volume when the slant height is given instead of the perpendicular height