# Designing an Open Box

## Activity

You are tasked to design a box by cutting squares from corners of an 8" by 6" rectangular cardboard. Use the applet below to investigate the box and choose the dimensions that you think best. Once you are decided, answer the questions below.

## Questions

1.) What are the dimensions of your final box? Why did you choose such dimensions? 2.) How did you calculate for the length, width, and height of the box? 3.) If we let x be the side length of the square (height of the box), what expressions represent the length and width of the box? What expression represents its volume? 3.) Can we cut out rectangles (not squares) from the corners of the rectangular cardboard? Why? 4.) What is the size of the smallest square that can be cut out from the corners of the rectangular cardboard and still make an open box? Do you think this size is appropriate? Why? 5.) What is the size of the largest square that can be cut out from the corners of the rectangular cardboard and still make an open box? Do you think this size is appropriate? Why?

## Note to the teacher

This applet can be used for teaching volume, polynomial expressions, and application of derivative. For elementary school and junior high schools, a prior activity where students will use papers to create boxes is recommended.