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.

Question

Mathematics

Celia Bird

6 November, 21:57

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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Trevon Williamson · Answer 1

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=pi*r^2 + 2pi*r*hV=pi*r^2*h or h=V / (pi*r^2) thenA=pi*r^2 + 2pi*r*V / (pi*r^2) to minimize surface area, we make dA/dr = 0try to do the rest, you'll find 2r = h