My brother wants to make an open-topped box out of a 4 × 6 square feet piece of cardboard by cutting identical squares from the corners and folding up the sides. What is the dimension of each square he will cut out of each corner in order to maximize the volume of the box he makes?
A) $\frac { 10 - \sqrt { 7 } } { 6 }$
B) $\frac { 10 + \sqrt { 7 } } { 6 }$
C) $\frac { 5 + \sqrt { 7 } } { 3 }$
D) $\frac { 5 - \sqrt { 7 } } { 3 }$

Question

Quizplus · Accepted Answer

The volume of the box is maximized when the size of the square cut from each corner is $\frac { 5 - \sqrt { 7 } } { 3 }$. This is derived by setting up the volume function V(x) = x(4-2x)(6-2x) and finding its critical points.

My Brother Wants to Make an Open-Topped Box Out of a 4