A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.

Question

What is the maximum volume this box could have? Here is my work. Do you agree?

 

Step 1: (50-2x)(10-2x)(x)

Step 2: 500-100x-20x+4x^2) (x)

Step 3: 4x^3-120x^2+500x

Step 4: dv/dx     12x^2-240x+500=0

Step 5: 3x^2-60x+125=0

Step 6: Quadratic formula x=[60 ± √2100]/6

x= 2.36 or 17.64

volume max: 45.28 * 5.28 * 2.36= 564 cm^3

Answer 1

You answer is correct, congratulations