Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}*pi*r^3[/tex]we have that
the diameter is reduced to half its original size
D=D/2
so
the new radius is
r=r/2
substitute in the formula of volume
[tex]V=\frac{4}{3}*p\imaginaryI *(\frac{r}{2})^3[/tex][tex]\begin{gathered} V=\frac{4}{3}*p\imaginaryI *\frac{r^3}{2^3} \\ V=\frac{1}{8}*\frac{4}{3}*p\imaginaryI *r^3 \end{gathered}[/tex]