Minimisation

A

amberzak

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A brewer wishes to market its beer in 500ml cylindrical cans. To minimise costs, the cans are to be made using the smallest amount of aluminium possible. Using differentiation, determine the dimensions of the can that the brewer should use.

I have a feeling it's something to do with finding the surface area, but when it says 500 ml cans, thats volume. So I'm a little confused.
 
Last edited:
amberzak said:
A brewer wishes to market its beer in 500ml cylindrical cans. To minimise costs, the cans are to be made using the smallest amount of aluminium possible. Using differentiation, determine the dimensions of the can that the brewer should use.

I have a feeling it's something to do with finding the surface area, but when it says 500 ml cans, thats volume. So I'm a little confused.
Click to expand...

A = 2*π*r*h + 2*π*r2

V = π * r2 * h → h = 500/(π*r2)

Now replace 'h' in 'A' - and you have a function with one variable.
 
[FONT=Verdana, Arial, Tahoma, Calibri, Geneva, sans-serif]A = 2*pi*r*(500/(pi*[/FONT]r2))+ 2*pi*r2

Is that right?
 
Thanks

I need to simplify, I guess

Then would it be where the derivative equals 0? I've forgotten how to do a minimum with derivatives.
 
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