Chapter 11.3, Problem 22PPS

To determine

To calculate: Area of the shaded sector.

Answer to Problem 22PPS

The area of the shaded sector is $334$ mm².

Explanation of Solution

Given information: Radius of the circle is YZ= $11.2$ mm and the angle of the shaded sector is ${360}^{\circ }-{55}^{\circ }={305}^{\circ }$ .

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, $r=11.2$ , $\theta ={305}^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector,

A $=\frac{305}{360}\times \frac{22}{7}\times {\left(11.2\right)}^2$

A $=\frac{305}{360}\times \frac{22}{7}\times 125.44$

A $=334$ mm²

Hence, area of the shaded sector is $334$ mm².