Use Cylindrical Coordinates to Find the Volume of the Solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64$

Multiple Choice

Use cylindrical coordinates to find the volume of the solid inside the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64$ and above the upper nappe of the cone $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$ .

A) $\frac { 512 } { 3 } ( 2 - \sqrt { 2 } )$
B) $\frac { 8 } { 3 } ( 2 - \sqrt { 2 } ) \pi$
C) $\frac { 512 \sqrt { 2 } } { 3 } \pi$
D) $512 ( 2 - \sqrt { 2 } ) \pi$
E) $\frac { 512 } { 3 } ( 2 - \sqrt { 2 } ) \pi$