How do you construct a 12-ounce cylindrical can with the least amount of material?
1 Answer
I will do this only in metric units, but the idea will be clear.
Let's say we use
For the can (closed-topped) we need:
a top, a bottom and the outer surface.
Let's call
Then the volume will be:
The total surface area
Top+bottom:
Side surface:
Total:
Since the volume is given, we can express
Differentiating, we get
This leads to:
Answer :
Diameter:
Checking the answer:
(close enough, with the rounding we've done)
Remark :
With the ounces and inches, you will have a lot of converting to do. I suggest you start by converting ounces to cubic inches.