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

question 176

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) \(\frac { 243 } { 8 } \pi ^ { 2 }\)

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