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

Multiple Choice

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) $\frac { 5 - \sqrt { 7 } } { 3 }$