quadratic model

Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares from each corner and folding up the sides. The box is to hold 9126 in33. How big a piece of cardboard is needed? 

Answer 1

9126 in^3 = volume = 6s^2

s^2 = 9126/6 = 1521

s = sqr1521= 39 inches

6 by 39 by 39 inch box

that's a 39+2(6) by 39+2(6) piece of cardboard

or 51 by 51 inch cardboard