Question 1051129
Sharon has a sheet of cardboard 16 cm long and 10cm wide.
 She cut four identical squares from the four corners and then folded the sides of the remaining shape up to form an open box.
 What is the maximum volume of the box that Sharon can make from her cardboard?
:
let x = the side of the square cut out
then the length and width of the box will be (16-2x) by (10-2x), the height = x
The volume equation, length * width * height
v = (16-2x)*(10-2x)*x
Foil
V = (160 - 32x - 20x + 4x^2)*x
V = x(4x^2 - 52x + 160)
V = 4x^3 - 52x^2 + 160x
The easiest way to find the max vol is by graphing this equation
{{{ graph( 300, 200, -2, 6, -10, 180, 4x^3-52x^2+160x) }}}
you can see max vol occurs when x=2, which is 144 cu/in