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 mass of the disk.
A)60$\pi$
B)96$\pi$
C)108$\pi$
D)120$\pi$
E)144$\pi$
F)180$\pi$
G)192$\pi$
H)240$\pi$

Question

Quizplus · Accepted Answer

The mass of the disk is found by integrating the density function over the area of the disk. In polar coordinates, the density function becomes $p(r, \theta) = r$, and the area element is $r \, dr \, d\theta$. The integral becomes $\int_0^{2\pi} \int_0^6 r^2 \, dr \, d\theta$, which evaluates to $144\pi$.

A Phonograph Turntable Is Made in the Shape of a Circular