Chapter 11.3, Problem 21PPS

To determine

To calculate: Area of the shaded sector.

Answer to Problem 21PPS

The area of the shaded sector is $322.14$ m²

Explanation of Solution

Given information: Radius of the circle is KJ= $15$ m and the angle of the shaded sector is ${164}^{\circ }$ .

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, $r=15$ , $\theta ={164}^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector,

A $=\frac{164}{360}\times \frac{22}{7}\times {\left(15\right)}^2$

A $=\frac{164}{360}\times \frac{22}{7}\times 225$

A $=322.14$ m²

Hence, area of the shaded sector is $322.14$ m²