Using polar coordinates to find the volume of the given solid

[serg_yegi]

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.

 

[Mark44]

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.

 

[serg_yegi]

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]

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.

 

[serg_yegi]

Ok. Is the actual integral correct?

 

[Mark44]

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