Use the method of [[../Cylindrical Shell Volumes|Cylindrical Shells]] to find the volume of the region bounded by the curves $y=x^3$, $y=8$, and $x=0$ about the $x-axis$. $\huge \begin{align} x &= 0 \\ y &= 8 \\ h(x) &= \brt{3}{y} \\ \\ V&= 2\pi \int_{0}^{8} y\pa{\brt{3}{y}}\d x \\ &= 2 \pi \pa{ \frac{3}{7} y^{ \frac{7}{3} } }\big \vert_{0}^8 \\ &= \frac{6\pi}{7}8^{ \frac{7}{3} } \end{align}$