You want derivation of cone volume?

Answer 1

This can be done easiest with integrals. Divide the cone into cylinders of very small height, and add up the volume of all the cylinders. Writing that as an integral will immediately give you the volume of the cone. For example, and for the simplifying case that the height is equal to the radius (r), you get the integral from x = 0 to r, of pi*x2. This integral is [(1/3)x3] with an upper limit of r and a lower limit of 0, or simply (1/3)r3.