- #1

Rikudo

- 120

- 26

- Homework Statement
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- Relevant Equations
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Why the area of the thin rings are ##2πasin\theta \, ds##? (a is the radius of the hollow sphere)

If we look from a little bit different way, the ring can be viewed as a thin trapezoid that has the same base length ( ##2πa sin\theta##), and the legs are ## ds##.

The angle between the leg and the lower base is ##90-\theta##. Hence,we can conclude that the height of the trapezoid is ##ds \, sin\theta##.

Since the base length is more or less the same, the area is just base x height.

This means, the area is :##2πa sin\theta \, ds \, sin \theta##.