# Thread: tricky math math question

1. ## tricky math math question

thanks for those who try and work on it
Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?

2. Originally Posted by anime_mania
thanks for those who try and work on it
Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?
I'll start you off.

obviously, this is an optimization problem in which we'd like to maximize the volume of a box. so the question is, what formula will give us the volume of the box for us to maximize? let's take this step by step

did you draw a diagram? (for related rates and optimization problems, ALWAYS draw a diagram if applicable--here, of course, it's applicable)

Let the side-length of the squares we cut out at each corner be $x$

then we have what you see in the diagram below.

we know that the volume of the box will be given by:

$V = \mbox{length} \times \mbox{width} \times \mbox{height}$

can you tell the length, width and height of the box from the diagram? if you can, there's your formula to maximize!