Chapter 11.3, Problem 29PPS

To determine

To find: The value of $x$ .

Answer to Problem 29PPS

The value of $x$ is $9.82$ ft.

Explanation of Solution

Given information: Radius of the circle is KJ= $x$ ft, angle of the shaded sector is ${152}^{\circ }$ and area of the shaded region is $128$ ft².

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, $r=x$ , $\theta ={152}^{\circ }$ and $\pi =\frac{22}{7}$

Area of shaded sector A $=\frac{\theta }{360}\times \pi r^2$

  $128=\frac{152}{360}\times \frac{22}{7}\times x^2$

  $x^2=\frac{128\times 360\times 7}{152\times 22}$

  $x^2=96.45$

  $x=9.82$ ft

Hence, the value of $x$ is $9.82$ ft.