A circle has an arc length of 2π in. The central angle for this arc measures π/6 radians.
What is the area of the associated sector?

answer: Area of sector is 37.68 inches²

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Length of arc = 2π inch

θ = π/6

2π = 360 degrees

π = 360/2 = 180

Therefore,

θ = 180/6 = 30 degrees

Therefore,

2π = 30/360 × 2 × π × r

Dividing both sides by π, it becomes

2 = 60r/360

60r = 2 × 360 = 720

r = 720/60

r = 12

The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Therefore,

Area of sector = 30/360 × 3.14 × 12²

= 37.68 inches²

0 is its x and y coordinate