Chapter 11.3, Problem 18PPS

To determine

To calculate: The area of the shaded region.

Answer to Problem 18PPS

The area of the shaded region is $10i{n}^2$ .

Explanation of Solution

Given information: The radius of the circle is $5in$ . Degree of the arc is ${46}^{\circ }$ .

Calculation:

From the given information, radius, $r=5in$ .

Degree of arc, $x={46}^{\circ }$ .

Area of a sector is given by, $A=\pi r^2\times \frac{x}{360}$

  $\begin{array}{l}A=\pi 5^2\times \frac{46}{360}\\ A=25\pi \times \frac{23}{180}\\ A=10\end{array}$

Area of shaded region, $A=10i{n}^2$

The area of the shaded region is $10i{n}^2$ .