Mensuration Problem

Question

The length of an arc of a circle is 12 cm. the corresponding sector area is 108 cm².

Find :

1. the radius of circle
2. the angle subtended at the center of the circle by the arc

Please Help !!!!!!

Answer 1

arc length = radius times radians = 12 (the angle measured in radians)

12 =rA where A= angle, r= radius

sector area = 108 = radius squared times one half the angle measured in radians

108 = r^2 times A/2

216 = r^2A = r(rA) =12r

r = 216/12 = 18 cm = radius

rA=12

18A=12

A=12/18=2/3 radian= 120/pi degrees = about 38.2 degrees

arc length = 12 = radius times angle = 18x(2/3) = 12 cm

sector area = 108 = r^2(A/2) = 18^2(2/3)/2 = 108 cm^2

radius = 18 cm

angle = 2/3 radian = 120/pi degrees = about 120/3.14159 = 38.2 degrees