Question

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.

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