An open box has a maximum capacity of 80 cubic centimeters. It is made from
a square piece of carton with 2-centimeter squares cut out from each of its four
corners. Find the dimensions of the original piece of carton.
original piece ---- x cm by x cm
sides of base of box --- (x - 4) cm each
volume of box = 2(x-4)^2
2(x-4)^2 = 80
(x-4)^2 = 40
x - 4 = √40
x = √40 + 4 = appr 10.3 cm
check:
side of base = 10.3 - 4 = 6.3
volume = 2(6.3)^2 = 79.38, slightly off due to round off of √40 + 4