Chapter 13.2, Problem 13P

A popular brand of soup comes in cans that are $2\frac{5}{8}$ in. in diameter and $3\frac{3}{4}$ in. tall. Each such can has a paper label that covers the entire side of the can (but not the top or the bottom).

1. If you remove a label from a soup can, you’ll see that it’s made from a rectangular piece of paper. How wide and how long is this rectangle (ignoring the small overlap where two ends are glued together)? Use mathematics to solve this problem, even if you have a can to measure. Explain your reasoning.
2. Ignoring the small folds and overlaps where the can is joined, determine how much metal sheeting is needed to make the entire can, including the top and bottom. Use the moving and additivity principles about area to explain why your answer is correct. Be sure to use an appropriate unit to describe the amount of metal sheeting