Chapter 11.3, Problem 28PPS

To determine

To find: The value of $x$ .

Answer to Problem 28PPS

The value of $x$ is ${54.93}^{\circ }\approx {55}^{\circ }$

Explanation of Solution

Given information: Radius of the circle is KL $=14$ in, angle of the shaded sector is $x^{\circ }$ and area of the shaded region is $94$ in².

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, $r=14$ , $\theta =x^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector,

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

  $94=\frac{x}{360}\times \frac{22}{7}\times {\left(14\right)}^2$

  $x=\frac{94\times 360\times 7}{22\times 196}$

  $x={54.93}^{\circ }\approx {55}^{\circ }$

Hence, the value of $x$ is ${54.93}^{\circ }\approx {55}^{\circ }$