Chapter 13.5, Problem 51E

To determine

To calculate: The area of sector of the circle.

Answer to Problem 51E

The area of sector of the circleis $54.7{\text{ feet}}^2$ .

Explanation of Solution

Given information:

The radius of circle is 8 feet and its central angle is $98°$ .

Formula used:

The area of sector of a circle of radius r and its central angle as $\theta$ is $A=\frac{1}{2}{r}^2\theta$ .

Calculation:

Consider the provided information radius of circle is 8 feet and its central angle is $98°$ .

Convert the angle to radian,

  $98\times \frac{\pi }{180}=1.71042\text{ radians}$

Recall that area of sector of a circle of radius r and its central angle as $\theta$ is $A=\frac{1}{2}{r}^2\theta$ .

Apply it,

  $\begin{array}{c}A=\frac{1}{2}{r}^2\theta \\ =\frac{1}{2}{\left(8\right)}^2\left(1.71042\right)\\ =54.7\end{array}$

Thus, the area of sector of the circle is $54.7{\text{ feet}}^2$ .