A Phonograph Turntable Is Made in the Shape of a Circular

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 $\pi$

Correct Answer:

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