Explanation
the volume of a hemisphere is given by:
[tex]\text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3[/tex]where r is the radius
then
[tex]\begin{gathered} Diameter=2\text{radius} \\ \frac{\text{Diameter}}{2}=r \\ \frac{24\text{ cm}}{2}=r \\ r=12\text{ cm} \end{gathered}[/tex]now, replace.
[tex]\begin{gathered} \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot r^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot(12\operatorname{cm})^3 \\ \text{Volume}_{hemisphere}=\frac{2}{3}\cdot\pi\cdot1728cm^3 \\ \text{Volume}_{hemisphere}=1152\text{ }\pi cm^3 \end{gathered}[/tex]so, the answer is
[tex]\text{Volume}_{hemisphere}=1152\text{ }\pi cm^3[/tex]I hope this helps you
