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a) Write an equation to represent the volume of an open box constructed by cutting congruent squares from the corners of a 24" by 14" piece of cardboard.

b) What is the domain of this model?

  • AFM (MATH) -

    let the side of the square to be cut out be x "
    then the
    length = 24-2x
    width = 14-2x
    height = x

    volume = x(14-2x)(24-2x)

    clearly domain is:
    x>0 and 24-2x>0 and 14-2x>0
    x>0 and x<12 and x<7

    so domain: 0 < x < 7

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