Solve the Problem B) C) D)

Multiple Choice

Solve the problem.
-Let D be the smaller cap cut from a solid ball of radius 9 units by a plane 3 units from the center of the sphere. Set up the triple integral for the volume of D in spherical coordinates.

A) $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 3 ) } \int _ { \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { d } \varphi \mathrm { d } \varphi \mathrm { d } \theta$
B) $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 9 ) } \int _ { 3 \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { de } \mathrm { d } \varphi \mathrm { d } \theta$
C) $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 9 ) } \int _ { \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { de } d \varphi d \theta$
D) $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 3 ) } \int _ { 3 \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { d } \operatorname { d } \varphi \mathrm { d } \theta$