Chapter 14, Problem 63RE

To determine

To calculate: The value of the triple iterated integral ${\displaystyle {\int }_0^{\pi }{\displaystyle {\int }_0^{\frac{\pi }{2}}{\displaystyle {\int }_0^{\sin \theta }{\rho }^2\sin \theta \cos \theta d\rho d\theta d\varphi }}}$.