the arc length and central angle of a circle are 10cm and 80degrees respectivly. what is the length of the radius?

Answer 1

Circumference of a circle

C = 2 r pi

the arc length

L = 2 r pi * theta / 360 °

= r * pi * theta / 180°

10 = r pi * 80 / 180 Multiply both sides by 180

10 * 180 = r * pi * 80

1800 = r * pi * 80 Divide both sides by 80 pi

1800 / 80 pi = r

r = 1800 / 80 pi

r = 40 * 45 / ( 40 * 2 * pi )

r = 45 / 2 pi

r = 45 / ( 2 * 3.14159 )

r = 45 / 6.28318

r = 7.162 cm