Complete Derivation of Mass Moment of Inertia of Hemisphere(Half Sphere) about the symmetric axis of Rotation.

Hi,

Problem: 
The top half of the sphere is created by rotating the circle of x2+y2=r2 around the y-axis. If the rigid body has mass m and density (rho), find the mass moment of inertia about y-axis in terms of m and rho. 





Solution: