Question

In a circle, of radius 9.5 cm, how long is an arc sub tended by a central angle measuring 5pi/12 radians?

Answer 1

The length of the arc is 12.43cm

Explanation:

First of all we need to calculate the circumference

To solve this problem we need to use the circumference formula of a circle:

c = circumference

r = radius = 9.5 cm

π = 3.14

c = 2π * r

we replace with the known values

c = 2 * 3.14 * 9.5cm

c = 59.66cm

The length of the circumference is 59.66cm

A complete circumference has 2pi radians

We divide 5pi/12 by 2pi and obtain the fraction of the total circle

(5pi/12) / 2pi = 5/24

we multiply this fraction with the circumference and obtain the length of the arc

59.66cm * 5/24 = 12.43cm

The length of the arc is 12.43cm