Question

select the correct answer arc located on circle has a length of 40 centimeters. the radius of the circle is 10 centimeters. what is the measure of the corresponding central angle for in radians? a. b. 3 c. d. 4

Answer 1

2 radians

Explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

let x be the central angle , then

arc = 2πr ×
`(x)/(2\pi )` ( cancel 2π on numerator and denominator )

= 2r × x

given arc length = 40 , then

2 × 10 × x = 40

20x = 40 ( divide both sides by 20 )

x = 2

the central angle has a measure of 2 radians