Calculus › Optimisation problems › Boxes of maximum volume

Cuboid of minimal surface area

High school · ●●●○○ 50 pts

A juice box is a rectangular box (cuboid) with volume 200 cm3200\ \text{cm}^3 (200200 ml). Find the length ll, width ww and height hh (in cm) of the box with the least possible surface area. Round each answer to five decimal places.

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optimizationsurface area and volumepartial derivativescritical points