maximizing the volume of a box

[hannahlisme]

[h=1]If i have an 8x11 piece of paper, how much of each corner should i cut off to have the maximum volume?[/h]

 

[Deleted member 4993]

If i have an 8x11 piece of paper, how much of each corner should i cut off to have the maximum volume?

You need to cut-off square shapes from the four corners to make the box.

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statment like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[HallsofIvy]

Since this has been here for several days now: Let a side of the square we cut out of each corner have length 'x'. Then we have cut a length x from each end of each side which originally had 11 now has length 11- 2x. similarly, each side which originally had length 8 now has length 8- 2x. So we have a "box" with sides of length 11- 2x, 8- 2x, and x and so volume x(11- 2x)(8- 2x). You can find the x that maximizes that by differentiating and setting the derivative equal to 0.

 

[lookagain]

If i have an 8x11 piece of paper,
how much of each corner should i cut off to have the maximum volume?

The problem stated does not define the situation well.

Assumptions:

1) The shapes to be cut out are square shapes.

2) There is to be an open box created by folding,
and that it will be a rectangular box.


The question could be amended to something closer to this**:

"If I have an 8" x 11" piece of paper, what side length of squares must
be cut off from each corner, so that the resultant open rectangular
box from folding will have the maximum volume?"



As the problem is stated, I can come up with a tray with slanted sides
(a type of open box) having a uniform depth (except in the areas down
to the slanted sides. There would be congruent cut-outs at the corners,
but not made in square shapes, so that when the sides are bent up,
the tray has slanted sides instead. And I could make this tray have a
greater volume than HallsofIvy's method and assumptions would give.




** Or the problem might be composed of one or two statements,
followed by a question to make it clearer to read.