A phonograph turntable is made in the shape of a circular disk of radius 6 inches with density function $p ( x , y ) = \sqrt { x ^ { 2 } + y ^ { 2 } }$ . Find the polar moment of inertia $I _ { 0 }$ of the disk.
A)2945.4$\pi$
B)3110.4$\pi$
C)3245.4$\pi$
D)3362.4$\pi$
E)3495.4$\pi$
F)3560.4$\pi$
G)3632.4$\pi$
H)3775.4$\pi$

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The Answer of A phonograph turntable is made in the shape of a circular disk of radius 6 inches with density function $p ( x , y ) = \sqrt { x ^ { 2 } + y ^ { 2 } }$ . Find the polar moment of inertia $I _ { 0 }$ of the disk.
A)2945.4$\pi$
B)3110.4$\pi$
C)3245.4$\pi$
D)3362.4$\pi$
E)3495.4$\pi$
F)3560.4$\pi$
G)3632.4$\pi$
H)3775.4$\pi$

A Phonograph Turntable Is Made in the Shape of a Circular