A thermal storage chest with a square base and a box-like shape must hold 20 ft 3 20\text{ ft}^3 of material. The bottom panel is made of reinforced insulation, which is three times more expensive per square foot than the side panels, while the top lid is constructed from a lightweight material that costs the same as the sides. Determine the side length s s s of the square base and the height h h h of the storage chest that will minimize the total material cost.

s = 10 3 ft s=\sqrt[3]{10}\text{ ft} h = 2 10 3 ft h=2\sqrt[3]{10}\text{ ft}

s = 10 3 ft s=\sqrt[3]{10}\text{ ft} h = 3 10 3 ft h=3\sqrt[3]{10}\text{ ft}

s = 3 10 3 ft s=3\sqrt[3]{10}\text{ ft} h = 2 10 3 ft h=2\sqrt[3]{10}\text{ ft}

s = 2 10 3 ft s=2\sqrt[3]{10}\text{ ft} h = 2 10 3 ft h=2\sqrt[3]{10}\text{ ft}

A thermal storage chest with a square base and a box-like shape m...

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