Chapter 11.3, Problem 23PPS

To determine

To calculate: Area of the shaded sector.

Answer to Problem 23PPS

The area of the shaded sector is $284.10$ in².

Explanation of Solution

Given information: Radius of the circle is PQ= $10.8$ in and the angle of the shaded sector is ${360}^{\circ }-{81}^{\circ }={279}^{\circ }$ .

Formula used: Area of sector $=\frac{\theta }{360}\times \pi r^2$

  $\theta =$ Angle of the shaded sector,

  $r=$ Radius of the circle.

Calculation:

Here, $r=10.8$ , $\theta ={279}^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector,

A $=\frac{279}{360}\times \frac{22}{7}\times {\left(10.8\right)}^2$

A $=\frac{164}{360}\times \frac{22}{7}\times 116.64$

A $=284.10$ in²

Hence, area of the shaded sector is $284.10$ in².