Chapter 9.2, Problem 5PSA

To determine

To find:The area of the sector AOB

Answer to Problem 5PSA

The area of the sector AOB is $39.27$ sq. units

Explanation of Solution

Given information:The following information has been given

The radius of the circle is five units $(r=5)$

A and B form a straight line as diameters

Calculation:We know that the measure of an arc is the degree measure subtended by the arc to the center of the circle. Hence, the angle subtended by the arc is same as the angle between the X and - X axes. Hence, we can say that

  $m\stackrel{⌢}{AB}={180}^0$

We know that the area of the sector can be found by

  $\stackrel{⌢}{AOB}=\pi r^2\frac{{180}^0}{{360}^0}$

Hence, we substitute the value of radius $(r=5)$ , and we get

  $\stackrel{⌢}{AOB}=\frac{25\pi }{2}=39.27$