Mozi Prompt of the Week

Algebra 2: Quadratics “Maximizing Volume”

You own a business that makes metal containers for your customers.

To keep costs low, your customer only wants to use 60’ of metal tubing to create a container in the shape of a square prism or an equilateral triangular prism. Your customer wants to know which prism will give him the container that will contain the maximum amount of volume.

First, create a square prism using 60’ of tubing (use x as the height and width of the prism and y as the length of the prism (see diagram http://map.mathshell.org/download.php?fileid=806) that will contain the maximum volume.

Then, create the equilateral triangular prism using 60’ of tubing (use x as the side of the triangle and y as the length of the prism (see diagram http://map.mathshell.org/download.php?fileid=806) that will contain the maximum volume.

Based upon your calculations, explain which configuration you will propose to your customer.