An open box with a square base is to have a volume of 18 ft3. (a) Find a function that models the surface area A of the box in terms of the length of one side of the base x.

Answer 1

if the base is square, then let's assume each side of the base is L

also assume the height of the box is H

the volume is then calculated as the base area times the height

volume = 18 = HLL = HL²

then H = 18/L²

the surface area of the box = the surface area of 2 bases + the surface area of 4 sides

surface area = 2 * L² + 4 * HL

surface area = 2L² + 4HL

since H = 18/L², then

surface area = 2L² + 4 * 18/L² * L

surface area = 2L² + 72/L