Chapter 9, Problem 8CR

To determine

To find the area of the region that can be irrigated through the sprinkler.

Answer to Problem 8CR

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

Explanation of Solution

Given:

The given angle is ${140}^{\circ }$ and the radius of the region is $35$ meters.

Calculation:

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 −

  $\begin{array}{l}\frac{\theta }{{360}^{\circ }}\times \pi r^2\\ =\frac{140}{{360}^{\circ }}\times \pi \times {35}^2\\ =1497\end{array}$

Therefore, the area of the sector is $1497$ square meters.