# Cone volume with triple integral

• December 18th 2012, 11:59 AM
BERMES39
Cone volume with triple integral
I have tried to calculate the volume of a cone with base radius "a" and height "h" using a triple integral. Either by hand or using a CAS calculator I get the same answer: a^2*h*pi. Can someone point out where is the error?
• December 18th 2012, 01:49 PM
a tutor
Re: Cone volume with triple integral
Why not use polar cylindrical ?
• December 18th 2012, 01:53 PM
ebaines
Re: Cone volume with triple integral
The height from the base to the surface of the cone is not $h-\frac h a y$, but rather should be $h - \frac h a \sqrt{x^2+y^2}$. And I agree - using polar coordintes would make the integral much simpler to evaluae.