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*h
V=pi*r^2*h or h=V/(pi*r^2)
then
A=pi*r^2 + 2pi*r*V/(pi*r^2)
to minimize surface area, we make dA/dr = 0
try to do the rest, you'll find
2r = h
Hope this help :D

Answer 2

Awesome thanks!

Answer 3

And you, are welcome.