Question

Circle A is shown with a central angle marked 30 degrees and the radius marked 5 inches. Which of the following could be used to calculate the area of the sector in the circle shown above?

Answer 1

Since the central angle of the sector of the circle is in degrees, we need to convert it to radians, so we are going to use the formula for the area of a circular sector: $A= \pi r^2( \frac{ \alpha }{360} )$
where 
$A$ is the area 
$r$ is the radius
$\alpha$ is the central angle

We know form our problem that the radius of the sector is 5 in, so $r=5in$. We also know that the sector's angle is 30°, so $\alpha =30$. Lest replace those value sin our formula: 
$A= \pi (5in)^2( \frac{ 30}{360} )$
$A=6.5in^2$

We can conclude that the expression we should use to calculate the area of the sector in the circle is: $A= \pi r^2( \frac{ \alpha }{360} )$