Find the volume obtained when the circle of radius 2 with center ( 2 , 0) is rotated about the y-axis.
A) $\frac{32}{3}$ $\pi$
B) $32$ $\pi$
C) $2 \pi$
D) $\frac{3}{32} \pi$
E) $\pi$

Question

Quizplus · Accepted Answer

The equation of the circle is $(x-2)^2 + y^2 = 4$. Solving for $x$, we get $x = 2 \pm \sqrt{4 - y^2}$. The volume of the solid of revolution is given by the integral $\pi \int_{-2}^{2} [(2 + \sqrt{4 - y^2})^2 - (2 - \sqrt{4 - y^2})^2] \, dy$, which simplifies to $\frac{32}{3} \pi$.

Find the Volume Obtained When the Circle of Radius 2 323\frac{32}{3}332​

Find the Volume Obtained When the Circle of Radius 2 $\frac{32}{3}$