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) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 8 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)

---

Definitions:

Hong Kong

A special administrative region of China, known for its vibrant cityscape, deep natural harbor, and extensive financial and trading centers.

Academic Locus of Control

A psychological construct that determines whether individuals attribute their educational success or failure to internal factors like effort, or external factors like luck.

Online College

Educational institutions that offer courses and degree programs through the internet, providing flexibility to study from anywhere.

Persist

To continue steadfastly or firmly in some state, purpose, course of action, or the pursuit of an objective, despite difficulties, obstacles, or discouragement.