1. The problem statement, all variables and given/known data Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin. 2. Relevant equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/x 3. The attempt at a solution So I know that the equation for the sphere is x2+y2+z2=a2 since it's centered at the origin and has a radius of a. And I'm pretty sure the integrand is 1, so the integral should look like ∫∫∫rdzdrdθ. For the limits of z, I solved for z in the sphere equation and got z=±√a2-x2-y2, which in cylindrical coordinates is z=±√a2-r2. Therefore the limits of integration for z are -√a2-r2 and +√a2-r2. The limits of r should be from 0 to a since a is the radius of the sphere. But I have no idea what the limits of θ are. Is it from 0 to 2π because it is a sphere? Advice would be appreciated. Thanks.