Answer
$\approx$ 599.5 $ft^{3}$
Work Step by Step
lateral area = $\pi$ $\times$ r $\times$ slant height
r = $\frac{96 \pi ft^{2}}{\pi 12 ft }$
r = 8 ft
h = $\sqrt (slant height)^{2} - r^{2}$
h = $\sqrt 144 ft^{2} - 64 ft^{2}$
h = 4 $\sqrt 5 $ ft
Volume = $\frac{\pi r^{2} h}{3}$
Volume = $\frac{\pi \times (8 ft)^{2} \times 4 \sqrt 5 ft }{3}$
Volume $\approx$ 599.5 $ft^{3}$
