Answer
$\displaystyle{V=\frac{\pi }{3}}\\ $
Work Step by Step
$\displaystyle{A\left(x\right)=\pi \left(x\right)^2}\\ \displaystyle{A\left(x\right)=\pi \left(x^2\right)}\\$
$\displaystyle{V=\int_{0}^{1}A\left(x\right)\ dx}\\ \displaystyle{V=\int_{0}^{1}\pi \left(x^2\right)\ dx}\\ \displaystyle{V=\pi \int_{0}^{1}x^2\ dx}\\ \displaystyle{V=\pi\left[\frac{1}{3}x^3\right]_{0}^{1}}\\ \displaystyle{V=\pi\left(\frac{1}{3}(1)^3-\frac{1}{3}(0)^3\right)}\\ \displaystyle{V=\frac{\pi }{3}}\\ $
