00:01
We're given a sheet of metal.
00:03
So let's go ahead and draw just a box to represent that metal.
00:08
And its dimensions are 20 by 12.
00:12
We're going to cut out a box, a corner.
00:15
Let's call it x is how much we're going to cut out.
00:17
So each of these we're cutting out x.
00:21
All of these.
00:22
They're all x.
00:24
And we want to determine the maximum possible volume of the box.
00:28
Well, the volume is going to be length times width times height.
00:34
Well, the length is going to be start off with 20, and we're going to take off 2x, and that's going to be the length of the box.
00:43
The width is going to be the same thing.
00:45
It's just 12 minus 2x.
00:48
And then the height is going to be how much we fold up, which is just x.
00:52
So let's do a little simplifying and find that the volume will be 12 times 20, which is 240.
01:04
I'm going to foil and then distribute the x as well...