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Math Help - Volume problem

  1. #1
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    Volume problem

    A rectangular sheet of metal measures 6cm by 8cm. Four equal squares are cut from each corner of the sheet (so it looks like a net of a rectangular prism, without the lid) and the remaining metal is bent to form an open ended rectangular tray. (so the equation of the volume would be V=4x(4-x)(3-x)]
    I) What would be the largest possible value of x?
    II) What would be the smallest possible value of x?

    Is there a way to do this without calculus?
    Last edited by requal; February 2nd 2009 at 04:02 AM.
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  2. #2
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    Quote Originally Posted by requal View Post
    A rectangular sheet of metal measures 6cm by 8cm. Four equal squares are cut from each corner of the sheet (so it looks like a net of a rectangular prism, without the lid) and the remaining metal is bent to form an open ended rectangular tray. (so the equation of the volume would be V=4x(4-x)(3-x)]
    I) What would be the largest possible value of x?
    II) What would be the smallest possible value of x?

    Is there a way to do this without calculus?
    The volume is calculated by:

    V(x)=x(8-2x)(6-2x)

    The three factors correspond to the edges of the box and must be positive (or zero).

    Therefore the smallest possible length of x is x = 0, but then the volume is zero too. Actually you leave the metal sheet untouched.

    The largest possible length of x is x = 3, but then the width of the box is zero and consequently the volume is zero too. Actually you fold the sheet of metal once.

    Thus the domain of V is d_V=[0, 3]
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