Question 604250
A rectangular box without lid is to be made from a square cardboard area of 300 cm squared by cutting equal squares from each corner and then folding up the sides What is the maximum volume?
:
A side of a square piece of cardboard: {{{sqrt(300)}}} = 17.32 cm, also means the base of the box will be square
let x = length of the side of the squares removed from the 4 corners
Dimension of the box; (17.32 - 2x) by (17.32 - 2x) by x
:
Vol = (17.32 - 2x)*(17.32 - 2x)*x
FOIL
V = {{{300 - 69.28x + 4x^2}}} * x
V = {{{4x^3 - 69.28x^2 + 300x}}}, is the equation
:
Graph this to find max volume
{{{ graph( 300, 200, -2, 10, -100, 500, 4x^3 - 69.28x^2 + 300x) }}}
:
max volume occurs when x = 2.9 and is very close to 385 cu/cm