The relation between the diameter (D) and the radius (r) is:
[tex]\begin{gathered} r=\frac{D}{2} \\ \text{ Substituting with D = 5 in:} \\ r=\frac{5}{2}\text{ in} \end{gathered}[/tex]The volume of a sphere is computed as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting with r = 5/2 in, we get:
[tex]\begin{gathered} V=\frac{4}{3}\pi(\frac{5}{2})^3 \\ V=\frac{4}{3}\pi(\frac{5^3}{2^3}) \\ V=\frac{4}{3}\pi(\frac{125}{8}) \\ V=65.45\text{ in}^3^{} \end{gathered}[/tex]