## Basic College Mathematics (9th Edition)

$V\approx 848.3~in^3$
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): $V=\frac{2}{3}*3.14*7.4^3$ $V\approx 848.3~in^3$