Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.

Correct result:

r =  9.9983 cm
v =  9.9983 cm

Solution:

V=3140 cm3 V=πr2 v v=V/(πr2) S=πr2+2 πrv S=πr2+2 πrV/(πr2) S=πr2+2 3140/r S=2 πr6280/r2 S=0 2 πr=6280/r2 2 πr3=6280 r=6280/(2π)3=6280/(2 3.1416)3 cm=9.9983 cm
v=V/(π r2)=3140/(3.1416 9.99832)=9.9983 cm



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