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 box. Find polynomials that represent the volume and outside surface of the box.
.
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.
.
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
.
if you look at the four corners of the "tic-tac-toe" looking paper, there are 4 identical squares, cut them out.
.
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.
.
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
.
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