A square has sides of 12 units squares of x1 by x1 units are...

Name: a square has sides of 12 units squares of x1 by x1 units are cut out of each corner and then the sides are folded up to create an open box express the volume of the box as a polynomial funct 92221
Uploaded: 2021-06-11T18:46:31-08:00
Duration: 2 min 39 s
Channel: Julie Silva
Description: a square has sides of 12 units squares of x1 by x1 units are cut out of each corner and then the sides are folded up to create an open box express the volume of the box as a polynomial funct 92221

A square has sides of 12 units. Squares of $x+1$ by $x+1$ units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of $x$. Volume of the box is calculated by multiplying height, length, and width. $V(x) = 4x^3 - 48x^2 + 144x$ $V(x) = 4x^3 + 48x^2 + 144x + 50$ $V(x) = 4x^3 - 36x^2 + 60x + 100$ $V(x) = 4x^3 - 40x^2 + 100x$

Transcript

00:01 So for this problem, it might be very helpful to draw our other picture.

00:04 So it says that suppose box is to be constructed from a square piece of material of side length paths.

00:09 So let's draw our square here.

00:11 And remember, because it's a square, all of the side lengths are x long.

00:17 Okay, well then we're told in order to make this box that we're going to cut out two inch squares from each corner.

00:23 So meaning that this would be two inches, this would be two.

00:27 Same for this corner.

00:30 The same will happen on the bottom left, and the same will happen for the bottom right.

00:35 Okay, so what we want to do is express the volume for this box.

00:39 Well, the box is going to be a rectangular prism.

00:41 And the way we find the volume is we multiply the length times the width times the height.

00:46 So let's start by talking about the length.

00:48 So that would be this distance right here for the box.

00:52 Well, remember, it started out its x inches, but we cut out two inches on this side and two inches on this side, meaning we cut out a total of four inches.

01:00 So that means that the length of this box will be x minus 4.

01:05 Okay, great.

01:06 We can substitute that in.

01:07 It's x minus 4.

01:09 Well, the same thing happened for the width.

01:12 Remember, it started at x inches, but we cut out two inches on these side.

01:17 So the width would also be x minus 4...