Answer
$\frac{124 \pi}{3} $
Work Step by Step
Set-up the integration using Disk method in terms of y and bounded by the equations.
$ \pi \int^{4}_{0} (5-y)^2 dy$
Limits of integration are in terms of y because the axis of rotation is vertical and bounded by the line y=4
$ \pi \int^4_0 (25-10y+y^2)dy$ , Integrate
$ \pi[ 25y - 5y^2 + \frac{y^3}{3} ] ^4_0$, Evaluate the definite integral
$ \pi [ (100-80+ \frac{64}{3}) -0 ]$
$ \frac{60}{3}+ \frac{64}{3} $
$\frac{124 \pi}{3} $
