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 answer:

r =  9.9983 cm
v =  9.9983 cm

Step-by-step explanation:

V=3140 cm3 V = π r2 v v = V/(π r2) S = π r2  + 2 π r v S = π r2 + 2 π r V /(π r2) S = π r2 + 2  3140 / r S = 2 π r  6280/r2 S=0 2 π r = 6280/r2 2 π r3 = 6280 r=36280/(2π)=36280/(2 3.1416) cm=9.9983 cm
v=V/(π r2)=3140/(3.1416 9.99832)=9.9983 cm

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