# Find volume of solid elliptic paraboloid using polar coordinates

1. May 22, 2012

### chris_usyd

1. The problem statement, all variables and given/known data
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..

2. May 22, 2012

### sharks

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.

3. May 22, 2012

### chris_usyd

thanks sharks