A cylindrical container with no lid must have a fixed volume

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A cylindrical container with no lid must have a fixed volume VV. The circular base is made of a material that costs three times as much per square inch as the material for the curved side. Determine the ratio of the container’s height hh to its base radius rr that minimizes the total cost of materials.

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