A water sprinkler sprays water over a distance of 40 feet wh

A water sprinkler sprays water over a distance of

40

feet while rotating through an angle of

degrees145°.

What area of lawn receives water?

Solution

Assume the lawn is a circle with radius = 40 ft.
---
Area of the whole circle = (pi)*40^2 sq.ft.
----

Proportion:

x/1600(pi) = 145/360
---
x = [1600pi][145/360]

= 644.4444448(pi) sq ft or 2024.58193  sq ft (area that receives water)