The Paper Bag Challenge
The Problem
The Problem
Company X has hired your firm to design a paper bag from an A3 piece of paper (30 cm by 42 cm). Their only requirement is that the bag has to have the maximum possible volume.
Company X has hired your firm to design a paper bag from an A3 piece of paper (30 cm by 42 cm). Their only requirement is that the bag has to have the maximum possible volume.
Explore!
Explore!
Use the applet below to observe how the net of the shopping bag affects the volume.
Use the applet below to observe how the net of the shopping bag affects the volume.
The Challenge
The Challenge
Let the length of the length of the base of the paper bag be x.
Let the length of the length of the base of the paper bag be x.
(i) Express the volume of the paper bag in terms of x.
(i) Express the volume of the paper bag in terms of x.
(ii) Plot the graph of volume against x.
(ii) Plot the graph of volume against x.
(iii) Find the maximum volume of the paper bag.
(iii) Find the maximum volume of the paper bag.