Question

The radius of a circle is 4 centimeters. What is the angle measure of an arc bounding a sector with area 2​ square centimeters?

Answer 1

Measure of the arc = 14.32°

Explanation:

Radius of a circle = 4 cm²

Area of the circle = πr²

Here, r = radius of the circle

Area of the circle = π(4)²

= 16π cm²

= 50.265 cm²

Since, area of a sector =
`(\theta)/(360)(\text{Area of the circle})`

Here, θ = Central angle subtended by the arc Or measure of arc

Area of the sector given as 2 cm²

2 =
`(\theta)/(360)(50.265)`

θ = 14.32°

Therefore, measure of the arc = 14.32°.