maths??

Let the radius be r and the height be h (both in cm). Then the volume is
200=π(r^2)h
Therefore h= 200/π(r^2).
Surface area is
A= 2*π(r^2)+2πrh
=2*π(r^2)+400/r
(The first term is for the two ends and the second term is for the side)
Differentiate with respect to r,
dA/dr = 4πr-400/r^2
To get minimun area, set dA/dr=0,
4πr-400/r^2=0
πr^3=100
r = (100/π)^(1/3)
and h=200/π(r^2) = 200*(100)^(-2/3) * π^(-1/3)

When the radius of the cylinder is root(3,200/pi)cm≈3.9929cm, it has the least surface area. The height of it is equal to the radius of it.
The surface area=2π*root(3,200/pi)*root(3,200/pi)+π*(root(3,200/pi))^2
=3π*(root(3,200/pi))^2 cm^2
≈3π*3.9929^2 cm^2
≈150.265cm^2