#### Joel wrote:

Can anyone help me, how to derive the formula of the volume of the cone 1/3*pi*r^2*h ?

The volume of a right circular cone with radius r and height h, equals the

area of the right triangle (let the base = r and the height = h), which is

being revolved along the line containing the line segment h, multiplied by the

circumference using the r/3 part of the centroid* as the radius of revolution.

The centroid of a triangle is where all of its medians intersect.

The centroid is the geometric center of the triangle.**

Then the formula for the volume is

the area of the triangle, multiplied by the circumference at the

geometric center (centroid), and using r/3 as the radius of revolution.

This is:

- - . . - - . . - - . . - - . . - - . . - - . . - - . . - -

* Suppose a right triangle is situated on the xy-plane with the

radius extending from (0, 0) to (r, 0) and the height extending

from (0, 0) to (0, h).

The x-coordinate of this centroid is r/3. (This can be worked out using

coordinate geometry.)

** Source:

http://en.wikipedia.org/wiki/Centroid