Evaluate the Spherical Coordinate Integral $\int_{0}^{\pi / 2} \int_{0}^{\pi / 2} \int_{0}^{9 \cos \varphi} \varrho^{2} \sin \varphi \mathrm{de} d \varphi d \theta$

Multiple Choice

Evaluate the spherical coordinate integral.
- $\int_{0}^{\pi / 2} \int_{0}^{\pi / 2} \int_{0}^{9 \cos \varphi} \varrho^{2} \sin \varphi \mathrm{de} d \varphi d \theta$

A) $\frac { 81 } { 2 } \pi ^ { 2 }$
B) $\frac { 243 } { 8 } \pi$
C) $\frac { 81 } { 2 } \pi$
D) $\frac { 243 } { 8 } \pi ^ { 2 }$