## Calculus (3rd Edition)

$\dfrac{16 \pi}{35}$
The volume of a revolution can be calculated as: $V=\pi \int_{m}^{n} (R^2_{outside}-R^2_{inside}) \ dy$ where, $R_{outside}=y^{1/3}$ and $R_{inside}=y^3$ Now, $V=\pi \int_0^1 (y^{1/3})^2 -(y^3)^2 \ dy =\pi \int_0^1 (y^{7/3} -y^6) \ dy =\pi [\dfrac{3 y^{5/3}}{5}-\dfrac{y^7}{7}]_0^1 \\=\dfrac{16 \pi}{35}$