Solve the Problem $\mathrm { D }$ Be the Region Bounded Below by the Cone

question 425

Multiple Choice

Solve the problem.
-Let $\mathrm { D }$ be the region bounded below by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ and above by the sphere $z = \sqrt { 81 - x ^ { 2 } - y ^ { 2 } }$ . Set up the triple integral in cylindrical coordinates that gives the volume of using the order of integration $\mathrm { dz } \mathrm { dr } \mathrm { d } \theta$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 9 } \int _ { 0 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 9 / \sqrt { 2 } } \int _ { 0 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)
• C) \(\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 9 / \sqrt { 2 } } \int _ { 0 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 9 } \int _ { 0 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)

---

Definitions:

Cirrhosis

Chronic, irreversible injury to liver tissue; commonly caused by frequent alcohol consumption.

Acute Diarrhea

A condition characterized by the abrupt onset of frequent, loose, water stools that lasts less than 14 days, often due to infection or toxin ingestion.

Protozoan

Heterotrophic, single-celled protist that moves by flagella, cilia, or pseudopodia.

Genetic Predisposition

An inherited increase in the likelihood of developing a particular disease based on one's genetic makeup.