The volume of a hemisphere is given by:
[tex]V=\frac{2}{3}\pi r^3[/tex]
where r is its radius.
In this case we know that the diameter is 48 in and we know that the radius is half the diameter, then we have:
[tex]\begin{gathered} r=\frac{48}{2} \\ r=24 \end{gathered}[/tex]
Plugging the value in the formula for the volume we have:
[tex]\begin{gathered} V=\frac{2}{3}\pi(24)^3 \\ V=\frac{2}{3}\pi(13824) \\ V=9216\pi \end{gathered}[/tex]
Therefore, the volume of the hemisphere is:
[tex]V=9216\pi\text{ cubic inches}[/tex]
