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?

Printable View

- Dec 18th 2012, 10:59 AMBERMES39Cone 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?

- Dec 18th 2012, 12:49 PMa tutorRe: Cone volume with triple integral
Why not use polar cylindrical ?

- Dec 18th 2012, 12:53 PMebainesRe: Cone volume with triple integral
The height from the base to the surface of the cone is not $\displaystyle h-\frac h a y$, but rather should be $\displaystyle h - \frac h a \sqrt{x^2+y^2}$. And I agree - using polar coordintes would make the integral much simpler to evaluae.