Find volume of solid elliptic paraboloid using polar coordinates

[chris_usyd]

Homework Statement

a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h. Its apex occurs at the point (0,0,h). Suppose a>=b. Calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.



2. The attempt at a solution
We normally do the questions that ask to find the volume of a cylinder. the polar coordinates are straight, which is x=rcos(), y=rsin();
but in this question, i don't how to set up the polar coordinates for x and y..

 

[DryRun]

Your equation for the elliptic paraboloid appears to be:
\frac{x^2}{a^2}+\frac{y^2}{b^2}\le \frac{h-z}{h}
Make z the subject of the equation to get the upper limit, as z varies from z = 0. The rest should be easy enough, as you are expected to use cylindrical coordinates to describe the volume.

 

[chris_usyd]

thanks sharks