# Using polar coordinates to find the volume of the given solid

1. Use polar coordinates to find the volume of the given solid.

2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

## Answers and Replies

Mark44
Mentor
1. Use polar coordinates to find the volume of the given solid.

2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
What have you tried? You have to show an effort first.

I've tried doing a double integral from theta=0 to theta=2pi and r=0 to r=4 of ((16-r^2)^(1/2))r (dr)(dtheta)

Mark44
Mentor
The limits of integration for r should be from r = 2 to r = 4. If you go from r = 0, you're getting the volume inside the cylinder, which you don't want.

Ok. Is the actual integral correct?

Mark44
Mentor
Yes, I don't see anything wrong with it.