Answer
$V\approx 848.3~in^3$
Work Step by Step
The solid shown is a hemisphere (half of a sphere).
We know that the volume of a sphere is given by:
$\displaystyle V=\frac{4}{3}\pi r^3$
Therefore, the volume of a hemisphere is half of this:
$\displaystyle V=\frac{1}{2}*\frac{4}{3}\pi r^3$
$\displaystyle V=\frac{2}{3}\pi r^3$
We plug in the radius ($7.4$ in):
$V=\frac{2}{3}*3.14*7.4^3$
$V\approx 848.3~in^3$
