Solve the Problem $D$ Be the Region Bounded Below by The $x y$

question 24

Multiple Choice

Solve the problem.
-Let $D$ be the region bounded below by the $x y$ -plane, above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 49$ , and on the sides by the cylinder $x ^ { 2 } + y ^ { 2 } = 36$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { dz } \mathrm { dr } \mathrm { d } \theta$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 36 - z ^ { 2 } } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 49 - z ^ { 2 } } } r d z d r d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 49 - r ^ { 2 } } } r d z d r d \theta\)

---

Definitions:

Productive

The effectiveness and efficiency in generating outcomes or results.

Norm Of Reciprocity

A social rule that suggests people should return favors and positive gestures with similar actions, fostering mutual cooperation and support.

Interest

The feeling of wanting to know or learn about something or someone.

Formal Leadership

Leadership that is officially sanctioned by an organization and comes with designated authority and responsibilities.