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

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