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2 problems match “surface area and volume”. Clear

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1. Open-top box with minimum surface area ●●○○○ 20 ptsA container company makes an open-top rectangular box with a square base. The box must have a volume of $108\ \text{cm}^3$. Let the side length of the square base be $x$ cm and the height be $h$ cm. (1) Find the value of $x$ that gives the minimum outer surface area. (2) Find the minimum surface area, in $\text{cm}^2$.
2. Cuboid of minimal surface area ●●●○○ 50 ptsA juice box is a rectangular box (cuboid) with volume $200\ \text{cm}^3$ ($200$ ml). Find the length $l$, width $w$ and height $h$ (in cm) of the box with the least possible surface area. Round each answer to five decimal places.