Chapter 11.3, Problem 19PPS

To determine

To calculate: The area of the shaded region.

Answer to Problem 19PPS

The area of the shaded region is $40.2c{m}^2$ .

Explanation of Solution

Given information: The radius of the circle is $8cm$ . Degree of the arc is ${72}^{\circ }$ .

Calculation:

From the given information, radius, $r=8cm$ .

Degree of arc, $x={72}^{\circ }$ .

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

  $\begin{array}{l}A=\pi 8^2\times \frac{72}{360}\\ A=64\pi \times \frac{1}{5}\\ A=40.2\end{array}$

Area of shaded region, $A=40.2c{m}^2$

The area of the shaded region is $40.2c{m}^2$ .