What is the formula for the volume of a cone?

The formula for the volume of a cone is \( V = \frac{1}{3} \pi r^2 h \).

To break this down, the volume \( V \) of a cone depends on two key measurements: the radius \( r \) of its circular base and the height \( h \) of the cone. The radius is the distance from the centre of the base to its edge, and the height is the perpendicular distance from the base to the tip (or apex) of the cone.

The formula \( V = \frac{1}{3} \pi r^2 h \) can be understood by comparing it to the volume of a cylinder. A cylinder with the same base and height as the cone would have a volume of \( \pi r^2 h \). The cone's volume is exactly one-third of this, which is why we multiply by \( \frac{1}{3} \).

The symbol \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159. It represents the ratio of the circumference of a circle to its diameter and is crucial in calculations involving circles and circular shapes.

To use the formula, simply square the radius (multiply the radius by itself), multiply by \( \pi \), then multiply by the height, and finally, divide the result by 3. For example, if a cone has a radius of 3 cm and a height of 6 cm, its volume would be calculated as follows:

\[ V = \frac{1}{3} \pi (3)^2 (6) = \frac{1}{3} \pi (9) (6) = \frac{1}{3} \pi (54) = 18 \pi \]

So, the volume of the cone would be \( 18 \pi \) cubic centimetres, or approximately 56.55 cm³ when you multiply by the approximate value of \( \pi \).