How Do You Calculate the Volume of Solid B Bounded by Given Surfaces?

[Chibus]

Homework Statement

Sketch the solid B that lies inside the surface x^2 + y^2 = 1 and is bounded above and below by the surface x^2 + y^2 + z^2= 2^2. Then find the volume of B.

Homework Equations

projxy = projection onto the xy plane, proj zy = projection on the zy plane

The Attempt at a Solution

(See attached)

http://img511.imageshack.us/img511/440/chibusq.jpg

I just wanted to check whether my definition of the integration is correct, meaning:

1) Is the function of the integration right? (Since the circle on the xy plane is x^2 + y^2 = 1, I've used that)

2) Are the limits correct?

Thanks for any help!

 

[Chibus]

Any help?

I've converted the above integral into cylindrical coordinates and solved it, and I ended up with Pi*sqrt(3) as the solution. However, it doesn't match the answer of solving the cylinder by using the formula V(cyl)=pi*r^2*h = pi*(1)^2*2*sqrt(3) = pi*2*sqrt(3)