Answer
$\dfrac{625 \pi}{6}$
Work Step by Step
The shell method to compute the volume of a region: The volume of a solid obtained by rotating the region under $y=f(x)$ over an interval $[m,n]$ about the y-axis is given by:
$V=2 \pi \int_{m}^{n} (Radius) \times (height \ of \ the \ shell) \ dy=2 \pi \int_{m}^{n} (y) \times f(y) \ dy$
Now, $V=2\pi \int_{0}^{5} y^2 (5-y) \ dy\\= 2 \pi \int_0^5 (5y^2-y^3) \ dy \\=2 \pi [ \dfrac{5y^3}{3}-\dfrac{y^{4}}{4}]_0^5 \\=2 \pi [ \dfrac{5(5^3)}{3}-\dfrac{(5^{4})}{4}] \\=\dfrac{625 \pi}{6}$
