Korchemkina T. T.

In the queue under the rain, there were 11 people, each holding an umbrella. They stood close together, so the umbrellas of the neighbors touched (see fig).

![](https://cdn.mathpix.com/cropped/2024_05_06_83e2b9d825e20bcabe9eg-04.jpg?height=320&width=1975&top_left_y=2178&top_left_x=39)

The rain stopped, people closed their umbrellas and stood, maintaining a distance of 50 cm between neighbors. By what factor did the length of the queue decrease? People can be considered points, and umbrellas - circles with a radius of 50 cm.

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The length of the queue with umbrellas is made up of 11 diameters of umbrellas, which is 22 parts of radii, each 50 cm long. The length of the queue without umbrellas is 10 intervals between 11 people, with each interval also being 50 cm. Therefore, the length of the queue has decreased by a factor of 22:10=2.2.

## Problem

