The volume of a cone is given by the formula:
V=13πr2hV=\frac{1}{3}\pi r^2hV=31πr2h
where rrr is the radius of the circular base and hhh is the perpendicular height of the cone. This formula means that the volume of a cone is one-third of the volume of a cylinder with the same base radius and height.
Explanation
- The base of the cone is a circle, so its area is πr2\pi r^2πr2.
- Multiplying this base area by the height hhh gives the volume of a cylinder.
- Since the cone occupies one-third of that volume, the factor 13\frac{1}{3}31 is applied.
Additional notes
- If only the diameter ddd of the base is known, the radius is half of the diameter, r=d2r=\frac{d}{2}r=2d.
- The formula then becomes V=112πd2hV=\frac{1}{12}\pi d^2hV=121πd2h.
- The volume is measured in cubic units corresponding to the units of rrr and hhh, such as cubic centimeters (cm3cm^3cm3) or cubic meters (m3m^3m3).
This formula applies to both right circular cones and oblique cones as long as the height is taken as the perpendicular distance from the base to the apex.