Question

Find the area of each sector. Photo attached

Answer 1

Answer:

Area of sector: 48π in^2; Option D

Step-by-step explanation:

~ We can see that the bolded portion of the circle must be the the sector that we need to compute the area of... ~

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 ⇒ Area of Circle: 144π

2. Let us see this as a proportionality:

Degree of sector/ Degree of circle = Area of sector/ Area of circle

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,

Area of sector: 48π in^2