On a circle of radius 12cm, the length of the arc that subtends a central angle of 120 degrees is ( ? )pi cm

Answer 1

Given: Radius = 12 cm

Find: Length of arc that subtends a 120 degree central angle.

SOLUTION:

C = Circumference

C = pi*diameter

C = pi*(24)

The length of the arc, L,

compared to the Circumference, C,

is proportional to the central angle.

L / C = 120 / 360

L / (24*pi) = 120 / 360

L = (24*pi) * ( 120 / 360 )

L = (24*pi) * ( 1/3 )

L = 8*pi

The length of the arc is 8*pi cm.

Answer 2

An arc that subtends a central angle of 120 degrees has a length of 120/360 = 1/3 the length of the total circumference of the circle. We know the entire circumference of the circle is 2πr, which in this case is 2π*12 = 24π. Since the length of the arc we're measuring is 1/3 of the overall circumference of the circle, the length of the arc is 24π*1/3 = 8π.