Question

The circle with center O has a minor arc BSA with a length of 3pi/2 inches. The central angle is 40 degrees. what is the cicumference of the circle

Answer 1

We know the formula for arc length is

s = r theta were r is the radius and theta is the central angle in radians

Changing 40 degrees to radians

40 * pi/180 = 2pi/9

Using the formula for arc length we can find the radius

3 pi /2 = r * 2pi/9

Solving for r

3 pi/2 * 9/2pi = r

27/4 = r

We want to find the circumference

C = 2 * pi * r

C = 2 * pi * 27/4

C = 27 pi/2 inches

Answer 27pi/2 inches