(Solved):
(c) Prove that \[ K=\iiint_{V} z^{2}\left(x^{2}+y^{2}+z^{2}\right)^{5 / 2} d x d y d z=\frac{\pi}{ ...
(c) Prove that \[ K=\iiint_{V} z^{2}\left(x^{2}+y^{2}+z^{2}\right)^{5 / 2} d x d y d z=\frac{\pi}{65}, \] where the region of integration, \( V \), is the volume enclosed by the sphere \( x^{2}+y^{2}+z^{2}= \) \( z \)