Differentiation turns out to be:
(-200/r^2) + 4*pi*r = dSA

Set it to 0
(-200/r^2) + 4*pi*r = 0

Solve for r
0 = 4*pi*r - 200/r^2
0 = pi*r - 50/r^2
0 = (pi*r^3 - 50)/r^2
0 = pi*r^3 - 50
r^3 = 50/pi
r = (50/pi)^(1/3)