Volume of a Region inside a cylinder and sphere (Symbolic)

[xipe]

Homework Statement

Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b.
Set up an iterated integral for the volume of W

Homework Equations

x^2+y^2+z^2=b^2
x^2+y^2=a^2
0<a<b

The Attempt at a Solution

I converted to cylindrical coordinates and tried to set up the triple integral as follows
[rdzdthetadr], where -sqrt(b^2-r^2)<=z<=sqrt(b^2-r^2), 0<=theta<=2pi, 0<=r<=a. Am I at least on the right track for the integral? Any help is seriously appreciated. Thank you! :)
P.S. (<= is meant to be 'less than or equal to'), just figured I'd clarify :)

 

[LCKurtz]

Homework Statement

Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b.
Set up an iterated integral for the volume of W

Homework Equations

x^2+y^2+z^2=b^2
x^2+y^2=a^2
0<a<b

The Attempt at a Solution

I converted to cylindrical coordinates and tried to set up the triple integral as follows
[rdzdthetadr], where -sqrt(b^2-r^2)<=z<=sqrt(b^2-r^2), 0<=theta<=2pi, 0<=r<=a. Am I at least on the right track for the integral? Any help is seriously appreciated. Thank you! :)
P.S. (<= is meant to be 'less than or equal to'), just figured I'd clarify :)

That looks correct.

 

[xipe]

Thank you for the reply. I spend way longer than I should have on this problem. I thought it was more complicated than this, so I am happy that the solution was easier than expected. Cheers! :)