Answer
$\dfrac{ 72 \pi }{35}$
Work Step by Step
We need to integrate the integral as shown below:
$Volume = \int_{0}^{4} \pi (\sqrt x- \dfrac{x^2}{8}) ^2 dx \\=\pi [\dfrac{x^2}{2}-\dfrac{x^{(7/2)}}{14} +\dfrac{x^5}{320}]_0^4 \\=\pi (8-\dfrac{64}{7} +\dfrac{16}{5}) \\=\dfrac{ 72 \pi }{35}$
