SOLUTION: You construct an open box from a square piece of material by cutting four centimeter squares from the corners and turning up the sides. The volume of the box is 576 cubic centimete

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Question 978174: You construct an open box from a square piece of material by cutting four centimeter squares from the corners and turning up the sides. The volume of the box is 576 cubic centimeters. Find the dimensions of the square piece of material that you used to construct the box.
Found 3 solutions by josgarithmetic, KMST, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
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The folded up flaps form a 3 cm height.
Let x be the original edge length of the square material.

Base of the box has area %28x-2%2A3%29%5E2.
Volume, highlight%28x%28x-2%2A3%29%5E2=576%29.


You would simplify that and put into general form, and then look for roots according to Rational Roots Theorem. You are only interested in testing the POSITIVE roots.

That work or its further description will not be shown, unless you have trouble with that process.

Answer by KMST(5328) About Me  (Show Source):
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If the squares cut from the corners have sides measuring four centimeters,
the height of the box will be 4 cm.
If the sides of the original square piece of material measured x cm,
the bottom of the box will be a square with sides measuring x-2%2A4=x-8 cm.

The surface area of the bottom (in square centimeters) will be %28x-8%29%5E2 ,
and that, multiplied times the height of the box in cm, %284%29 ,
is the volume in cubic centimeters:
4%28x-8%29%5E2=576
Solving:
4%28x-8%29%5E2=576
4%28x-8%29%5E2%2F4=576%2F4
%28x-8%29%5E2=144
x-8=sqrt%28144%29
x-8=12
x=12%2B8
x=highlight%2820%29 .
So the box was made from a square piece of material with sides measuring highlight%2820cm%29 .

Answer by MathTherapy(10553) About Me  (Show Source):
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You construct an open box from a square piece of material by cutting four centimeter squares from the corners and turning up the sides. The volume of the box is 576 cubic centimeters. Find the dimensions of the square piece of material that you used to construct the box.
If 4 cm squares are cut from corners, then each original side is: highlight_green%2820.97056275%29 cm

If 4 squares with sides of 4 cm each are cut from corners, then each original side is: highlight_green%2820%29 cm