SOLUTION: A square peice of cardboard is formed into a box by cutting out 3 in squares from each of the corners and folding up the sides. If the volume of the box needs to be 126.75 cubic in

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Question 192021This question is from textbook
: A square peice of cardboard is formed into a box by cutting out 3 in squares from each of the corners and folding up the sides. If the volume of the box needs to be 126.75 cubic inches, what size square piece of cardboard is needed? This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If you cut 3-inch squares from each corner of the orginal square piece of cardboard, then the length of the side of the original square must be:
2(3)+x inches.
This means that the square bottom of the newly-formed box has to be x by x inches.
The volume of the new box can then be expressed as:
V+=+3%28B%29 where B is the area of the base of the square box and 3 is the height of the box.
But the area of the base of the box is just x%5E2 and the volume (V) of the box is given as 126.75 sq.in., so...
126.75+=+3x%5E2 Divide both sides by 3.
42.25+=+x%5E2 Take the square root of both sides.
x+=+6.5inches.
So the sides of the original box are 2(3)+x = 6+6.5 = 12.5 inches.