SOLUTION: An open box is made from an 8-by-10-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. If x represents the side length of the squares

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Question 255962: An open box is made from an 8-by-10-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. If x represents the side length of the squares, which of the following is a function giving the volume V(x) of the box in terms of x?
Answer by NRobinson(4) (Show Source):
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To make an open box we can cut squares out of the corners and fold the sides up. If x is the length of the side we are cutting then when we fold that side up, x will be the height (take a minute to think about what this looks like when you cut out the box length x and then fold that flap up. the x inch piece you cut is the amount you are folding up so that is the height.)
So x is the height. We are looking for the volume so we will also need the length and width since the formula for volume is the product (*) of length, width and height.
We cut off x inches off the length and width on each side (again think about what this looks like). We are taking 2x off each measurement (one x from each end). So now instead of a length of 8 inches, our length is 8-2x inches.
Similarly, our width of 10 inches was cut down by 2x also to give us 10-2x inches.
Now we have in terms of x the length, width and height. The volume is the product of these three, so substitute them in. Let V(x) be the volume.
V(x)=length* width *height= (8-2x)*(10-2x)*(x)
We'll simplify for fun- FOIL the first two

Distribute x over each term

Note that the volume is going to be in cubic inches (inch*inch*inch)=(inch^3)