HELP...Box problems in geometry

sady

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May 4, 2006
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My problem: Create a net for a box by cutting congruent squares from the corners of a rectangular piece of paper that is 8" by 10". Fold up the sides of your paper to form an open-topped box.
What are the dimensions of this box in terms of x? Length=? width=? height=?

Wriet an algebraic equation to represent the volume of this box.

Enter this equation in y1. What is a resonabla domain for this graph?

What is a resonable range? Graph y1.

What is the maximum volume for this box?

What is the surface area of the interior of this box?
 
x is the length of the congruent squares cut from each corner of the rectangular paper to make a box. Looks somethig like this...

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sorry about the diagram, got distorted after posting my reply. Anyway, imagine a square of side x cut off from each corner of a rectangle to make the box.
 
sady said:
sorry about the diagram, got distorted after posting my reply. Anyway, imagine a square of side x cut off from each corner of a rectangle to make the box.

Ok, where are you stuck? What have you done?
 
i figured that volume = L*W*H
V=(8-2x)(10-2x)(x) Is that right?

Now how do you write this as equation in y1, what is the domain and range?
 
Y1 = (8-2x)(10-2x)x

domain ...

first of all, x has to be greater than 0, or there is no box, correct?

now, think carefully ... what is the upper limit for x? remember, you can only cut out
a square so big that will allow you to fold up the sides.
 
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