Question

an open box is made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. write the volume of the box as a function of x if the material is 18 inches by 12 inches.

Answer 1

V = 4x⁴ - 60x³ + 216x²

Explanation:

V = length x width x height = l x w x h

let x = side of a cut-out square (all side are of a square are equal)

l = 18-2x

w = 12-2x

h = x

V = (18-2x)(12-2x)(x)

V = (18x - 2x²)(12x - 2x²)

V = 216x² - 36x³ - 24x³ + 4x⁴

V = 4x⁴ - 60x³ + 216x²