Question

What is the circumference

Answer 1

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.