Answer:
<em>Area of sector: 48π in^2; Option D</em>
Step-by-step explanation:
<em>~ We can see that the bolded portion of the circle must be the the sector that we need to compute the area of... ~</em>
Let us plan out this problem. If we were to find the area of the circle provided a radius of 12 inches, we could create a proportionality between the degree of the sector, and the degree of the circle ( 360 ) and the area of the sector and the area of the circle.
1. To calculate the area of this circle, let us apply the formula πr^2, such that r is 12 inches ( and let us keep π in terms of π ) ⇒ π * ( 12 )^2 ⇒ 144 * π ⇒ <em>Area of Circle: 144π</em>
2. Let us see this as a proportionality:
<em>Degree of sector/ Degree of circle = Area of sector/ Area of circle</em>
3. Now let us say x ⇒ Area of the sector. Substitute values into this formula, and solve for x through algebra:
120 / 360 = x / 144π,
120 * 144π = 360 * x,
17,280π = 360 * x,
x = 17,280π / 360,
<em>Area of sector: 48π in^2</em>
