00:02
All right, so you're looking to maximize the volume here.
00:05
The volume is going to be a volume of a cylinder.
00:08
Pi, r, square.
00:09
Usually we would say h, but we're going to use l because that's the concept for this package.
00:14
So the girth here, we need a substitution in one of these variables, right? the girth here is stated as the perimeter of the cross -section.
00:22
So that's going to be 2 pi r plus the length, l.
00:28
That has to equal 141, 141 inches.
00:34
So the easiest way to do here is to solve for l.
00:37
L will be 141 minus 2 pi r.
00:42
Okay, so we're going to put that into here.
00:45
Pir squared and then 141 minus 2 pi r.
00:51
We'll do a little simplification there.
00:53
Best thing to do here is distribute.
00:55
So we're going to see the volume is 141 pi r squared minus 2 pi squared r cubed...