Question

Can someone help explain the following question with better detail?
The standard kilogram is a cylindrical alloy of 90% platinum and 10% iridum. The density of alloy is p=21.56g*cm^-3. Design a strategy for finding the optimal height and radius for the standard kilogram keeping in mind that the surface is ocassionally cleaned of unwelcomed atoms(dust)

Answer 1

We know the density of the alloy to be 21.56g*cm^3. We also know the overall mass to be 1kg. You will want to find the height and radius of a cylinder that would, as I read the question, as small a surface area as possible, while still maintaining enough volume to reach the 1kg of mass.

Answer 2

In my interpretation, a sphere would be the best shape for the standard prototype, since it has the lowest surface area of any solid. But if it must be cylindrical, I agree with VirPriscus.

Answer 3

I seem to remember something from many years ago that if you double-differentiate a volumetric equations you can determine the optimum height and radius to minimise the surface area for a given volume....basicallly this is whyy baked bean/soup/veg/meat cans are always the same shape...it uses the minimum material for a given volume and thus reduces packaging costs to the smallest amount....will look into this and get back.

Answer 4

AS per the course notes: Ideally, this would be a sphere, but as spheres roll easily they become impractical, whereas cylinders have flat surfaces which prevent this.