## 31. If the Earth Were an Orange

Wrap a perfectly round orange with a red string. Then lengthen the string so that it encircles the orange, passing 1 meter away from its surface. Now wrap the Earth (we assume it is spherical) with a blue string and lengthen this string so that it encircles the Earth, passing 1 meter above the Earth's surface.

Which string, in your opinion, had to be lengthened by a greater amount - the red one or the blue one? 58
31. Let $r$ be the radius of an orange, and $R$ be the radius of the Earth, both expressed in meters. The red rope was previously equal to $2 \pi r$, and then we extended it to the length of $2 \pi(r+1)$, i.e., approximately 6.283 m (more precisely, $2 \pi$ m). The blue rope
![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-170.jpg?height=548&width=858&top_left_y=503&top_left_x=584)

was previously equal to $2 \pi R$, and then we extended it to the length of $2 \pi(R+1)$, i.e., again approximately 6.283 m.

The extension of both ropes is the same.