An Open Box Is Made from a 16 Inch $\times$ 16 Inch Piece of Cardboard by Cutting Equal Squares from 16

question 235

Essay

An open box is made from a 16 inch $\times$ 16 inch piece of cardboard by cutting equal squares from each corner and folding up the sides. For maximum volume, what size squares should be cut out?

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Definitions:

Phantom Pain

A sensation of pain that feels like it's coming from a part of the body that's no longer there, often experienced after limb amputation.

Referred Pain

A pain perceived at a location other than the site of the painful stimulus, due to the network of interconnecting sensory nerves.

Amputated Structure

A body part that has been surgically or traumatically removed.

Somatosensory Cortex

The somatosensory cortex is a region of the cerebral cortex involved in processing sensory information from the body, including touch, temperature, and pain.