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 :)

Guest Dec 4, 2018