If the central angle of a circle has measure 100° and makes a minor arc with length 25, what is the radius?

Question

If the central angle of a circle has measure 100° and makes a minor arc with length 25, what is the radius?

Answer 1

Convert the central angle to radians:

100 x π/180 = 100π/180 = 10π/18 = 5π/9

Use the arc length formula; S = rθ or r = s/θ

r = 25/(5π/9) = 25•9/(5π) = 45/π = 14.324

Answer 2

C = 2πr

(100 /360) C = (100 / 360) 2πr

25 = (5 / 18) 2πr

90 = 2πr

45 = πr

45 / π = r

Answer 3

Circumference of the circle is 2 π r

arc length = angle/360 * 2 π r = angle/180 * π r

25 = 100/180 π r

solve for r using π key on the calculator or 3.14

radius =~ 14.32