Question

A solid metal sphere of radius 32cm is melted down and recast to make 64 identical small spheres.what will be the radius of each small sphere?

Answer 1

`V_1=(4)/(3)\pi R^3\\\\R=32cm\\\\V_1=(4)/(3)\pi\cdot32^3=(131072)/(3)\pi\ (cm^3)\\\\V_2=V_1:64\\\\V_2=(131072)/(64)\pi:64=(131072)/(3)\pi\cdot(1)/(64)=(2048)/(3)\pi\ (cm^3)\\\\r=?\\\\V_2=(4)/(3)\pi r^3`


`(4)/(3)\pi r^3=(2048)/(3)\pi\ \ \ /:\pi\\\\(4)/(3)r^3=(2048)/(3)\ \ \ /\cdot(3)/(4)\\\\r^3=512\\\\r=\sqrt[3]{512}\\\\r=8\ (cm)\leftarrow answer`