Chapter 11.3, Problem 27PPS

To determine

To find: The value of $x$ .

Answer to Problem 27PPS

The value of $x$ is $12.96$ cm.

Explanation of Solution

Given information: Diameter of the circle is JL= $x$ cm, angle of the shaded sector is ${180}^{\circ }$ and area of the shaded region is $66$ cm².

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, $r=\frac{x}{2}$ , $\theta ={180}^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector,

A $=\frac{\theta }{360}\times \pi r^2$

  $66=\frac{180}{360}\times \frac{22}{7}\times {\left(\frac{x}{2}\right)}^2$

  $66=\frac{180}{360}\times \frac{22}{7}\times \frac{x^2}{4}$

  $x^2=\frac{66\times 360\times 7\times 4}{180\times 22}$

  $x^2=168$

  $x=12.96$ cm

Hence, the value of $x$ is $12.96$ cm.