An open box is to be made from a square piece of material by cutting four-centimeter squares from each corner and turning up the sides (see figure). The volume of the finished box is to be 576 cubic centimeters. Find the size of the original piece of material.

Answer 1

size of original piece of material:
x cm by x cm

after cut-out
base is (x-8) by (x-8)
height = x

V = x(x-8)^2 = 576
x^3 - 16x^2 + 64x - 576 = 0
Nasty equation to solve.
Have you learned any methods to solve a cubic?
Newton's Method is probably the best way, but you have to know Calculus.
or, you could use Wolfram if you just want the answer.
http://www.wolframalpha.com/