can anyone tell me how to do the add math project work about the aluminium cans?

Question

a company is manufacturer of cylindrical aluminium tins.The manager plans to reduce the cost of production.The production cost is proportional to the area of the aluminium sheet used.the volume that each tin can hold is 1000cm3.i hope sumone who have done this kind of project can help me.If possible i would like to know every inch of it including the conjecture and heuristic..

Answer 1

Difficult without paper, but the principle is to work out a formula for the total area of aluminium sheet which still maintaining 1000cm3 volume.

In the following, r = radius of cylinder and h = height of can.

Area of aluminium = 2*pi*r^2 [the top and bottom] + 2*pi*r*h [because 2*pi*r is the circumference of the can]

Because pi*r^2*h = 1000, you can substitute h = 1000/pi*r^2 into the Area equation.

Then differentiate with respect to r, and when dA/dr = 0, that's the most economical way to make the can.

It should turn out at close to r = 5.4; h = 10.9