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

Multiple Choice

Solve the problem.
-Let $\mathrm { D }$ be the region bounded below by the $x y$ -plane, on the side by the cylinder $r = 3 \cos \theta$ , and on top by the paraboloid $\mathrm { z } = 8 \mathrm { r } ^ { 2 }$ . Set up the triple integral in cylindrical coordinates that gives the volume of $\mathrm { D }$ using the order of integration $\mathrm { dz } \mathrm { dr } \mathrm { d } \theta$ .

A) $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 \cos \theta } \int _ { 0 } ^ { 8 r ^ { 2 } } r d z d r d \theta$
B) $\int _ { 0 } ^ { \pi / 4 } \int _ { 0 } ^ { 3 \cos \theta } \int _ { 0 } ^ { 8 r ^ { 2 } } r d z d r d \theta$
C) $\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 3 \cos \theta } \int _ { 0 } ^ { 8 r ^ { 2 } } r d z d r d \theta$
D) $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 3 \cos \theta } \int _ { 0 } ^ { 8 r ^ { 2 } } r d z d r d \theta$