Chapter 4, Problem 17RE

To determine

To find : The area of the sector of a circle of radius r and central angle $\theta$ .

Answer to Problem 17RE

  $\frac{500\pi }{3}$ square inches

Explanation of Solution

Given information: Radius r =20 inches and central angle $\theta ={150}^{\circ }$

Calculation:

We know that area of sector of a sector of radius r and central angle $\theta$ (measured in radians) is

  $A=\frac{1}{2}\theta r^2$

Now , central angle of the sector is

  $\theta ={150}^{\circ }=150\times \frac{\pi }{180}=\frac{5\pi }{6}$ radians

Therefore, area of sector of radius r =20 inches and central angle $\theta ={150}^{\circ }=\frac{5\pi }{6}$ radians is

  $A=\frac{1}{2}\times \frac{5\pi }{6}\times {\left(20\right)}^2=\frac{500\pi }{3}$ square inches