Answer
$\displaystyle{V=\frac{2\pi}{3}}$
Work Step by Step
$\displaystyle{A(y)=\pi(1)^{2}-\pi(y)^{2}}\\ \displaystyle{A(y)=\pi\left(1-y^{2}\right)}$
$\begin{aligned} V &=\int_{0}^{1} A(y) \ d y \\ V &=\int_{0}^{1} \pi\left(1-y^{2}\right) \ dy \\ V &=\pi \int_{0}^{1} 1-y^{2} \ d y \\ V &=\pi\left[y-\frac{1}{3} y^{3}\right]_{0}^{1} \\ V &=\pi\left(\left(1-\frac{1}{3}(1)^{3}\right)-\left(0\right)\right) \\ V &=\frac{2\pi}{3} \end{aligned}$
