[tex]V_1=\frac{4}{3}\pi R^3\\\\R=32cm\\\\V_1=\frac{4}{3}\pi\cdot32^3=\frac{131072}{3}\pi\ (cm^3)\\\\V_2=V_1:64\\\\V_2=\frac{131072}{64}\pi:64=\frac{131072}{3}\pi\cdot\frac{1}{64}=\frac{2048}{3}\pi\ (cm^3)\\\\r=?\\\\V_2=\frac{4}{3}\pi r^3[/tex]
[tex]\frac{4}{3}\pi r^3=\frac{2048}{3}\pi\ \ \ /:\pi\\\\\frac{4}{3}r^3=\frac{2048}{3}\ \ \ /\cdot\frac{3}{4}\\\\r^3=512\\\\r=\sqrt[3]{512}\\\\r=8\ (cm)\leftarrow answer[/tex]