A sector of a circle has an arc length of 8 pi inches and a central angle of 20 degrees, as shown. What is the circumference of the circle? Express the answer in terms of Pi.

Step-by-step explanation:

Arc length has a formula of

and we have all the info we need to solve for the radius, which we will then use in the circumference formula:

and simplifying a bit,

and a bit more,

. Multiply both sides by 9:

72π = πr . Divide both sides by π to get that

r = 72.

Now we will sub that into the circumference formula to find the circumference. Recall that C = 2πr.

C = 2π(72) so

C = 144π

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.