The formula for the volume of a cone is:
V=13πr2hV=\frac{1}{3}\pi r^2hV=31πr2h
where:
- rrr is the radius of the base of the cone,
- hhh is the perpendicular height of the cone,
- π\pi π is approximately 3.14159.
This formula states that the volume of a cone is one-third the volume of a cylinder with the same base radius and height
. In words, the volume equals one-third times the area of the circular base (πr2\pi r^2πr2) times the height hhh. If you know the diameter ddd instead of the radius, you can use r=d2r=\frac{d}{2}r=2d in the formula. Additionally, if the slant height LLL is known instead of the vertical height, you can find the height using the Pythagorean theorem:
h=L2−r2h=\sqrt{L^2-r^2}h=L2−r2
and then substitute into the volume formula:
V=13πr2L2−r2V=\frac{1}{3}\pi r^2\sqrt{L^2-r^2}V=31πr2L2−r2
This allows calculation of volume when slant height is given
. In summary, the standard and most commonly used formula is:
V=13πr2h\boxed{V=\frac{1}{3}\pi r^2h}V=31πr2h
which gives the volume of a cone in cubic units when rrr and hhh are in linear units
