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

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)   (Show Source): You can put this solution on YOUR website!
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 .
Volume, .

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)   (Show Source): You can put this solution on YOUR website!
If the squares cut from the corners have sides measuring four centimeters,
the height of the box will be cm.
If the sides of the original square piece of material measured cm,
the bottom of the box will be a square with sides measuring cm.

The surface area of the bottom (in square centimeters) will be ,
and that, multiplied times the height of the box in cm, ,
is the volume in cubic centimeters:

Solving:

.
So the box was made from a square piece of material with sides measuring .
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!
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: cm
If 4 squares with sides of 4 cm each are cut from corners, then each original side is: cm

RELATED QUESTIONS
An open box is to be made from a square piece of material, mc001-1.jpg inches on a side,... (answered by addingup)
An open box is to be made from a flat square piece of material 15 inches in length and... (answered by stanbon)
An open-top box will be made from a square piece of cardboard of length 26-inch by... (answered by ankor@dixie-net.com)
Volume. A flat, square piece of cardboard is used to construct an open box by cutting out (answered by jim_thompson5910)
An open box made from a square piece of cardboard 14 inches on a side by cutting... (answered by greenestamps,josgarithmetic,ikleyn)
You plan to make an open box by cutting equally sized squares from each corner of a... (answered by Edwin McCravy)
An open box is to be made out of a piece of cardboard 10 in by 15 in by cutting off equal (answered by ankor@dixie-net.com)
An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out... (answered by josgarithmetic,ikleyn)
An open box is to be made from a flat square piece of material 14 inches in length and... (answered by stanbon)