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Minimize Cost for Bottom of Cylindrical Can

The metal used to make the top and bottom of a cylindrical can costs 4 cents/in^2, while the metal used for the sides costs 2 cents/in^2. The volume of the can is to be exactly 100 in^3. What should the dimensions of the can be to minimize the cost of making it?

Could you please show all work so I can better grasp the concept? Thank you.

Solution Preview

Assume the radius of the top and bottom of the can is r, and the height is h.
First, we find the area of the top and bottom of the can by
St = 2*(π * r^2) = 2π* r^2
The area of the side is Ss = ...

Solution Summary

The Cost for a Cylindrical Can is minimized. All work is shown.