A closed cylindrical can must contain of liquid

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A closed cylindrical can must contain 1000 cm31000\text{ cm}^3 of liquid. The side material costs $0.03\$0.03 per cm2\text{cm}^2, and the top and bottom material cost $0.06\$0.06 per cm2\text{cm}^2. Calculate, to the nearest tenth of a centimetre, the radius that minimizes the total cost of the material.

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