The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. $x^{2}+(y-1)^{2}=1^{2}$ about the y-axis
A) $V=\frac{4}{3} \pi$
B) $V=\frac{8}{3} \pi$
C) $V=\frac{28}{3} \pi$
D) $V=\frac{1}{3} \pi$
E) $V=\frac{20}{3} \pi$

Question

Quizplus · Accepted Answer

The given equation is a circle centered at (0,1) with radius 1. When rotated about the y-axis, it forms a sphere with radius 1. The volume of a sphere is $\frac{4}{3} \pi r^3$, where $r=1$. Thus, the volume is $\frac{4}{3} \pi$.

The Region Bounded by the Given Curves Is Rotated About x2+(y−1)2=12x^{2}+(y-1)^{2}=1^{2}x2+(y−1)2=12

The Region Bounded by the Given Curves Is Rotated About $x^{2}+(y-1)^{2}=1^{2}$