Vhemisphere = (2/3) pi * r^3 .....so
Vhemisphere / [ (2/3) pi] = r^3 take the cube root of both sides
( Vhemisphere / [ (2/3) pi] )^(1/3) = r
The surface area of a hemisphere =
2 * pi * r^2 ....substiute for r
2 * pi * [ ( Vhemisphere / [ (2/3) pi] )^(1/3) ] ^2 =
2 * pi * [ ( Vhemisphere / [ (2/3) pi] )^(2/3) ]