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.

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