Question

On circle C points A and B are separated by an arc whose length is 18 centimeters. If the radius of C is 8 centimeters, what is the measure of central angle 0 in radians

Answer 1

2.25 radians

Explanation:

First we need to find the length of the circunference, using the formula:

C = 2 * pi * r

Where r is the radius. Using r = 8, we have:

C = 2 * pi * 8 = 50.2655 cm

Now, to find the measure of the central angle related to that arc of 18 cm, we can use a rule of three, knowing that the whole circunference has a central angle of 2pi radians:

2pi rad -> 50.2655 cm

x -> 18 cm

x = 18 * 2pi / 50.2655

x = 2.25 rad