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# How could I find the area of the sector watered?

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Here's the problem:

A rotating water sprinkler makes one revolution every 15 s. The water reaches a distance of 5 m from the sprinkler.

a) What is the arc length of the sector watered when the sprinkler rotates through _ 5π 3 ? Give your answer as both an exact value and an approximate measure, to the nearest hundredth.

For this question, I got $${25π \over 3}$$ as the exact value and $$≃ {26.18}$$ as the approximate measure.

b) Show how you could find the area of the sector watered in part a).

This is the part where I got confused? How should I solve for this? The textbook did this:

How did they get this formula? Or is this just something I need to memorize?

Thank you :)

Dec 4, 2018