A cylindrical container must hold of liquid

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A cylindrical container must hold 2000 cm32000\text{ cm}^3 of liquid. The top and bottom disks are made from a material that costs twice as much per square centimeter as the material used for the side. If the cost per square centimeter of the side material is kk, which radius rr minimizes the total manufacturing cost? (a) r=1000π cmr=\sqrt{\tfrac{1000}{\pi}}\text{ cm} (b) r=(1000π)1/3 cmr=\bigl(\tfrac{1000}{\pi}\bigr)^{1/3}\text{ cm} (c) r=(500π)1/3 cmr=\bigl(\tfrac{500}{\pi}\bigr)^{1/3}\text{ cm} (d) r=(250π)1/3 cmr=\bigl(\tfrac{250}{\pi}\bigr)^{1/3}\text{ cm}

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