3 Questions
Explain the process of making an open box from a 20cm by 20cm piece of cardboard as described in the text.
To make an open box, one needs to cut out four squares from the corners of the 20cm by 20cm piece of cardboard and fold the flaps.
What is the biggest volume of box that can be made from a 20cm by 20cm piece of cardboard using the described method?
The biggest volume of box that can be made using this method is when the squares cut out from the corners are as large as possible, which results in a cube with a volume of 8000cm³.
Is there a relation between the size of the paper and the size of the square cutout that produces the maximum volume? If so, what is it?
Yes, there is a relation between the size of the paper and the size of the square cutout that produces the maximum volume. The larger the paper, the larger the square cutout needed to produce the maximum volume of the box.
Explore the maximum volume achievable for an open box made from cutting a 20cm by 20cm piece of cardboard and folding the flaps. Investigate the relationship between the size of the cardboard and the size of the square cutout for maximizing the volume. Extend the exploration to rectangular sheets of paper for a deeper analysis.
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