Chapter 12.6, Problem 7P

Penguins huddle together to stay warm in very cold weather. (See Figure 12.85 .) Suppose that a certain type of penguin has a circular cross-section approximately 14 inches in diameter (so that if you looked down on the penguin from above, the shape you would see would be a circle, 14 inches in diameter). Suppose that a group of this type of penguin is huddling in a large circular cluster, about 20 feet in diameter. (All the penguins are still standing upright on the ground; they are not piled on top of each other.)

 

Figure 12.85 Penguins in a huge cluster.

1. Assuming that the penguins are packed together tightly, estimate how many penguins are in this cluster. (You might use areas to do this.) Is this an overestimate or an underestimate? Explain.
2. The coldest penguins in the cluster are the ones around the circumference. Approximately how many of these cold penguins are there at any given time? Explain.
3. So that no penguin gets too cold, the penguins take turns being at the circumference. How many minutes per hour does each penguin spend at the circumference if each penguin spends the same amount of time at the circumference? Explain.