00:01
Here, we're told that we have a piece of cardboard, and we want to cut out the corners.
00:08
We don't know how much we're going to cut out.
00:09
We're just going to cut out x from each of the corners.
00:12
And then we're going to fold those up to create a box.
00:15
Well, the original box is an 8 by 10.
00:17
This is the original cardboard is 8 by 10.
00:21
So what is going to be the volume of this box? because we want to maximize that volume.
00:28
Well, the volume is always going to be the length times the width, times the height.
00:34
And the length, if we take 8 and we take away two of the xes, we take away those red lines.
00:41
So the length is going to be 8 minus 2x.
00:43
Whatever x is, we take away to them.
00:46
And we're going to do the exact same thing with the width, because we're going to take away two of the xes.
00:52
So that's going to be 10 minus 2x.
00:55
So you can see that x has to be some number between 0 and 4.
00:59
And then the height is just going to be x, because that's what we fold up.
01:03
So that tells me that the volume will be, let's go ahead and distribute that...