An open rectangular box with square base is to be made from 300 cm² of material. What dimensions will result in a box with the largest possible volume? A) 2 cm × 2 cm × 37 cm B) 10 cm × 10 cm × 5 cm C) 6 cm × 6 cm × 11 cm D) 11 cm × 11 cm × 7 cm E) 1 cm × 1 cm × 75 cm

Question

Quizplus · Accepted Answer

The volume of a box is maximized when its dimensions are as close to each other as possible, given a fixed amount of material. For an open box with a square base, the material used will be for the base and the four sides. Given the constraint of 300 cm² of material, option B) 10 cm × 10 cm × 5 cm offers dimensions that are closest to each other, leading to a more efficient use of material for volume maximization.

An Open Rectangular Box with Square Base Is to Be