Chapter 9.3, Problem 11PSA

To determine

To find: The area of a sector $MOG$ .

Answer to Problem 11PSA

The area of the sector in a given circle is 25 ${\text{π units}}^2$

Explanation of Solution

Given information :

  $\begin{array}{l}\text{Radius of circle (}r\text{) }=10\text{ units}\\ \text{Arc angle (}\theta )={90}^{\text{o}}\\ \text{Area of a circle}=\pi r^2\end{array}$

Formula used :

Area of the sector of a circle = $\frac{\text{θ}}{{360}^o}\times (\text{Area of circle})$

Calculation :

  $\text{Area of the sector }MOG=\frac{\theta }{{360}^{\text{o}}}\times (\text{Area of the circle})$

  $\begin{array}{l}=\frac{{90}^o}{{360}^o}\times \pi r^2\\ =\frac{{90}^o}{{360}^o}\times \pi \times {10}^2\\ =25\pi {\text{ units}}^2\end{array}$