SOLUTION: A square piece of cardboard is 16 inches on a side. A square piece x inches on a side is cut out from each corner. The flaps are then turned up to form an open boz. Find polynomial

Question 264580: A square piece of cardboard is 16 inches on a side. A square piece x inches on a side is cut out from each corner. The flaps are then turned up to form an open boz. Find polynomials that represent the volume and outside surface of the box.
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
A square piece of cardboard is 16 inches on a side. A square piece x inches on a side is cut out from each corner. The flaps are then turned up to form an open box. Find polynomials that represent the volume and outside surface of the box.
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if you make a visual from a square peice of paper it will help understanding
on the square piece of paper draw to parallel lines horizontal and 2 vertical to make a "tic-tac-toe" looking paper. you should see 9 identical squares.
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16 is the length of 3 squares
"A square piece "x" inches on a side is cut out from each corner"
If u look at the corners and label the sides as "x" you will notice that 3x=16 so x=16/3 or 5.333333333333333333333333333333
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if you look at the four corners of the "tic-tac-toe" looking paper, there are 4 identical squares, cut them out.
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now your paper should look like a plus(+) made up of 5 identical squares.
If you were to fold them up to the middle to make a square box, you will notice there is no top.
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to get volume use the formula V=LWH which means volume=length times width times hieght. if you look at the box you will notice that the length width and hieght are all = to "x" so V=(x)(x)(x) or V=x^3
So replace "x" with 16/3 or 5.3333. I will show in both forms:
V=(16/3)(16/3)(16/3) 16x16x16=4096 3x3x3=27 4096/27=V
V=(5.3333)(5.3333)(5.3333)= 151.700859277
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to find the outside surface area(A) of the box, you know there are 5 squares that make up the box, each square has the side "x" or 16/3
so we would find the area of 1 square and multiply by 5 so 5x^2=A
16x16=256 3x3=9 so (256/9)=x^2
5(256/9)=A
1280/9=A

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