The surface of a cylinder with an open upper side is:
O = pi×R2+2×pi×R×H,
where R is the radius of the cylinder and H is the height. The volume is given,
V = 30 = pi×R2×H liters (or dm3).
The surface can then be written as O = pi×R2+2×V/R.
If you take the first derivative of R and look where this derivative equals 0 you get Rmin = (V/pi)1/3.
So the minimum surface is O = pi×Rmin2+2×pi×Rmin×H = 3×pi1/3×V2/3 or about 42.42 dm2.
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