Consider the volume bounded by the sphere of radius R (with center $r_0$ = R/2 z) and the plane z = 0.
Evaluate $\int dS$ over the surface of the truncated sphere.
I'm not sure how to integrate over the partial sphere.
I need to find with to plug in for dS, as well as the limits of integration.
I know in spherical coordinates you would be integrating theta from 0 to π, and phi from 0 to 2π, and dS = $r^2$sinθdθdϕ. I'm just not sure how to go about removing the part of the sphere below the z=0 plane. Since the sphere is centered at R/2 z, the area below the z=0 plane is no longer half of the sphere, so I can't just change the limits of theta to 0 to π/2.
Could put dS in cartesian coordinates (dxdydz)?