Find the volume of the indicated region.
-the region enclosed by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$ and the cylinder $( x - 5 ) ^ { 2 } + y ^ { 2 } = 25$
A) $\frac { 2000 } { 9 } ( 3 \pi - 4 )$
B) $\frac { 500 } { 3 } ( 3 \pi - 4 )$
C) $\frac { 2000 } { 3 } ( 3 \pi - 4 )$
D) $\frac { 625 } { 3 } ( 3 \pi - 4 )$

Question

Quizplus · Accepted Answer

The correct answer is A because the volume of the region enclosed by the sphere and the cylinder is the volume of the sphere minus the volume of the cylinder. The volume of the sphere is $\frac { 4 } { 3 } \pi r ^ { 3 } = \frac { 4 } { 3 } \pi ( 10 ) ^ { 3 } = \frac { 4000 } { 3 } \pi$. The volume of the cylinder is $\pi r ^ { 2 } h = \pi ( 5 ) ^ { 2 } ( 10 ) = 250 \pi$. Therefore, the volume of the region enclosed by the sphere and the cylinder is $\frac { 4000 } { 3 } \pi - 250 \pi = \frac { 2000 } { 3 } ( 3 \pi - 4 )$.

Find the Volume of the Indicated Region x2+y2+z2=100x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100x2+y2+z2=100

Find the Volume of the Indicated Region $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$