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 =
or about 42.42 dm2.
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