Polynomial Models: Open Box
View the Lesson | MATHguide homepage Updated December 18th, 2016

Status: Waiting for your answers.

Given:You have a cardboard sheet that is 53 inches long by 41 inches wide.
Problem:Congruent squares (x by x square inches in size, red in color in the diagram above) are cut from the corners of the cardboard. Once cut, the cardboard is folded upward to form an open box.
  • What is the length of the squares that must be cut in order to maximize the volume of the open box?
  • What is the maximum volume of the open box?
Solution:x = inches   [Report responses to the nearest tenth.]
Vmax = cubic inches