A large sheet of cardboard 2 m by 4 m will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What is the largest possible volume of such a box? A) 1.2180 m³ B) 1.4001 m³ C) 1.5396 m³ D) 1.6247 m³ E) 1.3241 m³

Question

Quizplus · Accepted Answer

The volume of the box can be maximized by setting the derivative of the volume function with respect to the side length of the squares cut out equal to zero and solving for that side length. The volume of the box is given by $V = x(2 - 2x)(4 - 2x)$, where $x$ is the side length of the squares cut out. Differentiating and finding the maximum gives the largest possible volume, which is 1.5396 cubic meters.

A Large Sheet of Cardboard 2 M by 4 M