Use Polar Coordinates to Find the Volume of the Solid $x ^ { 2 } + y ^ { 2 } = 16$

Multiple Choice

Use polar coordinates to find the volume of the solid inside the cylinder $x ^ { 2 } + y ^ { 2 } = 16$ and the ellipsoid $2 x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = 64$ .

A) $943.21$
B) $843.21$
C) $1,043.21$
D) $793.21$
E) $693.21$