use the method of disks ...
$\displaystyle \displaystyle V = \pi \int_a^b [r(x)]^2 \, dx$
where $\displaystyle r(x)$ is the radius of a representative disk formed by rotating the curve ... in this case, $\displaystyle r(x) = -x^2 + 11x - 24$ , $\displaystyle a = 3$ , and $\displaystyle b = 8$.