Question

Use spherical coordinates. let h be a solid hemisphere of radius 1 whose density at any point is proportional to its distance from the center of the base. (let k be the constant of proportionality.) (a) find the mass of h.

Answer 1

Whereas the density of the hemisphere at any point is proportional to it's density, then 

 The full answer in attachment, we use the partial integral using the spherical coordinates, 

and we find that the mass of h = πK/2