Suppose that an open box with a volume of 1500cm3 is to be constructed by taking a
piece of cardboard 20cm by 40cm, cutting squares of side length x can from each corner, and folding up the sides.
Two different ways, and find the exact dimensions of the box in each case.
If the volume of the box is 1500cm3, then
x(40−2x)(20−2x)=1500Model(40−2x2)(20−2x)=1500Distribute x800x−80x2−40x2+4x3=1500Apply FOIL method800x−120x2+4x3=1500Combine like terms200x−30x2+x3=375Divide both sides by 4x3−30x2+200x−375=0
The, by using synthetic division and trial and error with the factor of 375,
Thus,
x3−30x2+200x−375=0(x−5)(x2−25x+75)=0
So if x=5, then
40−2x=3020−2x=10
Therefore, the exact dimension of the box is 5 by 30 by 10cm.
No comments:
Post a Comment