There are two (equivalent) formulas for the circumference of a circle:
C = 2 pi r, where r is the radius of the circle
C = pi d, where d is the diameter of the circle
In this particular problem, however, we're dealing with arc length. For the shown central angle "theta" = 160 degrees, the arc length is 42 cm.
Knowing this enables us to calculate the radius or diameter of the circle.
Arc length = s = (radius) (central angle, in radians, not degrees)
First, convert 160 degrees to radians: 160 deg pi rad
----------- * ------------ = (8/9) pi rad
1 180 deg
Then 42 cm = r *(8/9) pi rad
Solve for the radius (r): divide 42 cm by (8/9) pi rad
Then use the formula for circumference introduced earlier:
C= 2 pi r Substitute [42 cm / ( (8/9) pi rad )] for r.
Simplify your result, and you will then have the circumference, C, in cm.
