What is the maximum volume of a square box from an 18cm by 12cm board?

Question

Finding the dimensions of a square box with maximum volume on an 18cm by 12cm board

Answer 1

Easy solution is this:

 

Vol = l x w x d, let that be x^3, since in a square box, l = w = d.

 

So, x^3 = 18 x 12

 

 x^3 = 216

 

x = 6

 

So, I think you could cut the 18cm length into 3 even pieces, each 6 cm by 12 cm, and then cut each of those into 2 pieces that are 6 by 6.  You now have six 6 x 6 cm pieces.