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The standard kilogram is in the shape of a circular cylinder with its height equal to its diameter. Show that, for a circular cylinder of fixed volume, this equality gives the smallest surface area, thus minimizing the effects of surface contamination and wear.

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syed514

Well, it can be easily done by differentiating function of area with respect to one of either height or radii/diameter (if calculus is enabled).say:A=pir^2 + 2pirhV=pir^2h or h=V/(pir^2)thenA=pir^2 + 2pirV/(pir^2)to minimize surface area, we make dA/dr = 0try to do the rest, you'll find 2r = h

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