Find the volume of the indicated region.
-the region enclosed by the paraboloids $z = x ^ { 2 } + y ^ { 2 } - 4$ and $z = 94 - x ^ { 2 } - y ^ { 2 }$
A) $9604 \pi$
B) $4802 \pi$
C) $7203 \pi$
D) $2401 \pi$

Question

Quizplus · Accepted Answer

The volume is found by integrating the difference of the two functions over the region where they intersect. The intersection occurs when $x^2 + y^2 = 49$. The volume is $\int_{0}^{49} \pi (94 - 2r^2 - (-4)) \, dr = 2401 \pi$.

Find the Volume of the Indicated Region z=x2+y2−4z = x ^ { 2 } + y ^ { 2 } - 4z=x2+y2−4

Find the Volume of the Indicated Region $z = x ^ { 2 } + y ^ { 2 } - 4$