Chapter 9, Problem 13CT

To determine

To find the arc length and area of a sector with given radius and angle.

Answer to Problem 13CT

The area of the sector is $1497$ square meters.

Explanation of Solution

Given:

The given angle is $\theta ={40}^{\circ }.$ and the radius of the region is $r=13$ inches.

Calculation:

The arc length is given by the following formula −

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\times 2\pi r\\ =\frac{40}{{360}^{\circ }}\times 2\pi \times 13\\ =9.08\end{array}$

So, the arc length is $9.08$ inch.

It is known that the area of the sector is given by the following formula

  $\frac{\theta }{{360}^{\circ }}\times \pi r^2$

Where $r$ is the radius of the sector.

So, applying the above formula, the following is the area of the sector obtained −

  $\begin{array}{l}\frac{\theta }{{360}^{\circ }}\times \pi r^2\\ =\frac{40}{{360}^{\circ }}\times \pi \times {13}^2\\ =118\end{array}$

Therefore, the area of the sector is $118$ square inches.