Question

A cardboard box manufacturer makes open boxes from rectangular pieces of cardboard of size 30cm by 40cm by cutting squares from the four corners and turning up the sides.

A) find a mathematical model expressing the volume of the box as a function of the length of the side of the square to be cut out.
B) what is the domain of your function in part a?

Answer 1

let the length of the side to be cut out be x cm

length = 40-2x
width = 30-2x
height = x

Volume = x(40-2x)(30-2x)

b) clearly, all of the factors must be positive number
so 30-2x>0
-2x > -30
x < 15 and of course x > 0

so 0 < x < 15