a) Write an equation to represent the volume of an open box constructed by cutting congruent squares from the corners of a 24" by 14" piece of cardboard.

Question

b) What is the domain of this model?

Answer 1

let the side of the square to be cut out be x "
then the
length = 24-2x
width = 14-2x
height = x

volume = x(14-2x)(24-2x)

clearly domain is:
x>0 and 24-2x>0 and 14-2x>0
x>0 and x<12 and x<7

so domain: 0 < x < 7