The Iterated Integral $\int_{0}^{\frac{\pi}{2}} \int_{0}^{2 \cos ^{2} \theta } \int_{0}^{4-r^{2} } r \sin \theta d z d r d \theta$

Multiple Choice

The iterated integral $\int_{0}^{\frac{\pi}{2}} \int_{0}^{2 \cos ^{2} \theta } \int_{0}^{4-r^{2} } r \sin \theta d z d r d \theta$
is

A) $\frac { 57 } { 45 }$
B) $\frac { 56 } { 45 }$
C) $\frac { 53 } { 45 }$
D) $\frac { 52 } { 45 }$
E) $\frac { 51 } { 45 }$