Textbook Problem

Area of a Sector of a Circle In Exercises 53 and 54, use the following information. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure).

For a circle of radius r, the area A of a sector of the circle with central angle $\theta$

(in radians) is given by $A=\frac{1}{2}{r}^2\theta$.

Sprinkler System A sprinkler in a garden is set to spray water over a distance of 25 feet and rotates through an angle of $120°$. Find the area of the region.