A cylindrical can is made from tin.If it can be contain $1000 m^3$ liquid inside it then what is the parameter of design if we are oblige use the minimum amount of tin. My teacher give me this and say that cocacola used this. I can understand that it can be solved by maxima & minima.But how.Help me please.
2026-03-25 17:40:20.1774460420
Find out the design of a cylinder
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Let us suppose that your can is a perfect cylinder. Let say that "r" is the radius and "h" the height. The area of the top is Pi r^2; same for the bottom. The area of the side is 2 Pi r h. Then, the total area of the cylinder is 2 Pi r (r + h) and its volume is Pi r^2 h. But you know that the volume is 1000. This gives you a relation between "r" and "h", isn't ? So, eliminate "h" from the equation which gives the volume and replace "h" by the so obtained value in the formula which gives the total area. Then, now, the total area became just a function of "r" and you want to minimize it. Can you continue with this ?