SOLUTION: A box is to be removing four identical squares (with side length X) from each corner of a retangular piece of card then folding up the resulting flaps. If the piece of card is 40cm

Algebra ->  Functions -> SOLUTION: A box is to be removing four identical squares (with side length X) from each corner of a retangular piece of card then folding up the resulting flaps. If the piece of card is 40cm      Log On


   

Question 498879: A box is to be removing four identical squares (with side length X) from each corner of a retangular piece of card then folding up the resulting flaps. If the piece of card is 40cm by 30cm write down a fundtion for the volume of the resulting box in terms of X. What sort of funtion is it ( quadratic, Rational, cubic or...). What is the domain of this funtion?

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
After removing the corner squares of side x, the remainder of the sides of the original rectangular cardboard will measure (40-2x) and (30-2x) and the height of the finished box will be x.
The volume of this box can be expressed as:
V+=+%2840-2x%29%2830-2x%29x If you multiply these factors, you'll get:
V+=+4x%5E3-140x%5E2%2B1200x
Clearly, this is a "cubic" function.
From a practical standpoint, x cannot equal or exceed half the length of the smaller side of the original rectangle, otherwise, you could not make a box.
So x can take on values: 0%3Cx%3C15