Mathematics

Mathematics

Problem

A closed right circular cylinder must hold 1000 cm31000\text{ cm}^3 of liquid. The material for the top and bottom costs \0.05persquarecentimeter,whilethematerialforthesidecosts0.05 per square centimeter, while the material for the side costs 0.02 per square centimeter. Determine the radius (to the nearest hundredth of a centimeter) that minimizes the total cost of materials.

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