SOLUTION: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 6 in. by 10 in. by cutting out equal squares of side x at each corner and then fol

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Question 393540: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 6 in. by 10 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

Volume of a box=length*width*height

We can easily see that the height of the box will be x.

What about the length and the width?

The length should be 10 inches minus x inches minus x inches, since there would be two x's cut out of the length.

The width should be 6 inches minus x inches minus x inches, since there would be two x's cut out of the width as well.

So, we have:

height=x

length=10-2x

width=6-2x

Volume=x%2A%2810-2x%29%2A%286-2x%29 inches cubed

V=4x%5E3-32x%5E2%2B60x inches cubed

You can multiply those terms out using the FOIL method and you will end up with the correct answer.

In some cases, it might be easier to leave the Volume in that first factored form.

I hope this helps!