1. ## Can someone please show me how to do this?

An open box with a square base is constructed from a square piece of cardboard 24 inches on a side by cutting out a square from each corner of the cardboard and turning up the sides. express the volume V as a function of the length x of the side of the square cut from each corner.

2. Originally Posted by wayneo1688
An open box with a square base is constructed from a square piece of cardboard 24 inches on a side by cutting out a square from each corner of the cardboard and turning up the sides. express the volume V as a function of the length x of the side of the square cut from each corner.
You know that each square has a side of length x. So two of those are taken from each side of the cardboard, right? Thus when the side pieces are folded up the remaining base is a square with sides of length 24 - 2x.

I'll leave it to you to figure out the height of the box and the volume.

-Dan

3. ## Express volume

thanks, but how do i express the volume as a function of the length x of the side of the square cut from each corner?

4. Originally Posted by wayneo1688
thanks, but how do i express the volume as a function of the length x of the side of the square cut from each corner?
The volume of a rectangular solid is given by
$V = lwh$
where l is the length of the base, w is the width of the base, and h is the height of the solid.

You have a square base, so $l = w = 24 - 2x$. When you fold the corners up (each having a length of x) what height does that give you for the box? (If you can't see this immediately you are over-thinking the problem. It's obvious.)

-Dan