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

Question 360

Multiple Choice

Solve the problem.
-Let D\mathrm { D } be the region that is bounded below by the cone φ=π4\varphi = \frac { \pi } { 4 } and above by the sphere ϱ=6\varrho = 6 . Set up the triple integral for the volume of D\mathrm { D } in cylindrical coordinates.


A) 02π06r36r2rdzdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { r } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta
B) 02π06/2036r2rdzdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 / \sqrt { 2 } } \int _ { 0 } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta
C) 02π06036r2rdzdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta
D) 02π06/2r36r2rdzdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 / \sqrt { 2 } } \int _ { r } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta

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