Chapter 6.2, Problem 44E

To determine

To find: the area of the sector.

Answer to Problem 44E

  $47.5{\text{ cm}}^2$

Explanation of Solution

Given information:

  $\begin{array}{c}\text{Central angle}\left(\theta \right)=105°\\ \text{Radius}\left(r\right)=7.2cm\end{array}$

Calculation:

Convert degree into radian by multiplying the degree by $\frac{\pi }{180°}$ as shown below.

  $\begin{array}{c}\theta =105°\left(\frac{\pi }{180°}\right)\\ =\frac{7\pi }{12}\end{array}$

Thus $105°$ is $\frac{7\pi }{12}$ radian.

The area of sector $\left(A\right)$ is evaluated as follows:

  $\begin{array}{c}A=\frac{1}{2}{r}^2\theta \\ =\frac{1}{2}{\left(7.2\right)}^2\left(\frac{7\pi }{12}\right)\left[\text{Put the value of }r\text{ and }\theta \right]\\ =\frac{1}{2}\left(51.84\right)\left(\frac{7\pi }{12}\right)\\ =47.5{\text{ cm}}^2\end{array}$

Thus the area of the sector is $47.5{\text{ cm}}^2$ .