Answer
$\displaystyle{V=\frac{264\pi}{5}}$
Work Step by Step
$\displaystyle{x^3=8}\\
x=2$
$\displaystyle{V=\int_{0}^{2}(2\pi (3-x))\left(8-x^3\right)\ dx}\\
\displaystyle{V=2\pi\int_{0}^{2}x^4-3x^3-8x+24\ dx}\\
\displaystyle{V=2\pi\left[\frac{1}{5}x^5-\frac{3}{4}x^4-4x^2+24x\right]_{0}^{2}}\\
\displaystyle{V=2\pi\left(\left(\frac{1}{5}(2)^5-\frac{3}{4}(2)^4-4(2)^2+24(2)\right)-(0)\right)}\\
\displaystyle{V=\frac{264\pi}{5}}$
