An open box is to be formed by cutting four identical squares from the corners of a sheet of metal 25 cm by 32 cm, and folding up the metal to form sides.

Question

Write a function that models the volume of the box.

What is the maximum volume that the box can hold?

The capacity of the box must be 1575 cm³ and the height must be less than 5cm. What is the side length of the squares removed?

Answer 1

V = x(25-2x)(32-2x)

=x(800 -114x +4x^2)

= 800x -114x^2 +4x^3

V'(x) = 800 -228x + 12x^2

3x^2 - 57x +200 = 0

x = 57/6 +/-(1/6)sqr(57^2 - 12(200))

= (56 +/-75.16)/12

= 19.16/6

=3.19 cm which is less than 5 cm

= box height= side length of squares removed