math grade 12
posted by karen .
A open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Derermine the dimensions of the square that must be cut to create a box with a volume of 100cm3. Widht= 20-2x, length =30-2x, height=x.
just plug the values into the equation
100 = x(20-2x)(30-2x)
4x^3 - 100x^2 + 600x - 100 = 0
x^3 - 25x^2 + 150x - 25 = 0
There are 3 real solutions, approximately
0.17, 9.52, 15.31
15.31 is out, since the sides aren't long enough.
Not an easy problem, if you have no tools for solving cubics.