# Question #f0ea3

$\frac{1024 \pi}{625}$
The region bounded by the given curves has been shown in the attached figure in red shade. Now consider an elementary strip of width $\delta x$ shown in blue pen in the figure. Its length would be $y = 16 - \left(16 - {x}^{2}\right) = {x}^{2}$. If this strip is revolved around y=16, the volume of the elementary disc so formed would be $\pi {\left({x}^{2}\right)}^{2} \delta x$
The volume of the solid so generated would be ${\int}_{x = o}^{4} \pi {x}^{4} \mathrm{dx}$
= $\pi {\left({x}^{5} / 5\right)}^{4} = \frac{1024 \pi}{625}$