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

Multiple Choice

Use polar coordinates to find the volume of the solid under the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and above the disk $x ^ { 2 } + y ^ { 2 } \leq 4$ . Select the correct answer.

A) $64 \pi$
B) $5.3 \pi$
C) $32 \pi$
D) $16 \pi$
E) $8 \pi$