Consider making an open box from a 16" by 48" rect

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ochocki

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Consider making an open box from a 16" by 48" rectangular piece of cardboard by cutting equal sized squares from each corner and folding up the sides. let x be the side of the squares that are cut out.


Write the function V which gives the volume of the box as a function of x.


What is the real world domain of V?


I am having a really hard time setting this up. I know the volume formula but don't really know how to apply it. If the length and width are provided I think the height would be x. I can't really find the value for X. Can someone help me set this up so I can find these values?

Thanks
 
Did you draw a picture?

x = Height
Length = 48" - 2x
Width = 16" - 2x

Volume = Height*Length*Width
 
That's kind of what I came up with. Does this look right?

x(48-2x)(16-2x)

then I suppose through foiling and then distributing the X I would get an equation that I can graph in my calculator, am I anywhere close?
 
"foiling"? What is that? I suppose you mean simple multiplication.

Why do you have to multiply it out or expand it? Can't your calculator take it in this form? Just remember to use multiplication between the parentheses. Your calculator may not understand "implied" multiplication. You may also have some trouble with the Domain. I hope it is obvious that x > 0". It is a little less obvious that x < 8". Do you see why?
 
Thanks for the help by the way. I think im getting there, when I input the term i get the same result both factored and non. It's a huge parabola. I am still not understanding how to get the value for x. the only number I came up with was x=16. this makes no sense to me though, it just feels wrong. I really struggle with these story problems, please excuse the lack of logic I may portray.
 
You should not have a parabola. It is a cubic equation - degree 3.

I am quite pleased that you get the same graph two different ways. This is a great confidence builder.

You may have some scale problems as you are interested in 0 < x < 8, but the volume goes all the way up to nearly 1300!

You should not be getting x = 16. How are you getting that? Have you restricted the Domain to 0 < x < 8? There is no way to get x = 16 from that. x = 16 for what, by the way?

Let's review the problem statement.

"Write the function" - You have done that.

"What is the Domain" - I have told you that, but you have not demonstrated an understanding of why this is so.

You do not need to graph anything on this one. Look at your drawing and tell me why the Domain is as I have suggested. You will then be done with this problem.
 
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