Solve the Problem $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } r d z d r d \theta$

question 4

Multiple Choice

Solve the problem.
-Let D be the smaller cap cut from a solid ball of radius 9 units by a plane 8 units from the center of the sphere. Set up the triple integral for the volume of D in cylindrical coordinates.

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 17 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } \mathrm { rdzdrd \theta }\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 17 } } \int _ { 8 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 8 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)

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The two primary factors that influence an individual's development, including genetic makeup and external factors like upbringing and culture.

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