To find the volume of a cone, you can use the formula:
Volume (V) = (1/3) × π × r² × h
Where:
- V is the volume of the cone.
- r is the radius of the base of the cone.
- h is the height of the cone.
- π is a mathematical constant approximately equal to 3.14159.
Let’s break it down:
The formula for the volume of a cone is derived from the formula for the volume of a cylinder, which is V = π × r² × h. Since a cone can be thought of as a pyramid with a circular base, its volume is one-third of that of the cylinder that encloses it. Thus, we include the factor of 1/3 in the formula.
To calculate the volume:
- Measure the radius (r) of the base of the cone.
- Measure the height (h) of the cone from the base to the tip.
- Plug the values of r and h into the formula.
For example, if the radius of the base is 3 units and the height is 5 units, the volume calculation will go like this:
V = (1/3) × π × (3)² × (5) = (1/3) × π × 9 × 5 = (1/3) × 45π = 15π units³.
This means the volume of the cone is 15π cubic units.