Question

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.

Answer 1

Answer:

Step-by-step explanation:

Arc length has a formula of

$AL=\frac{\theta}{360}*2\pi r$ and we have all the info we need to solve for the radius, which we will then use in the circumference formula:

$8\pi=\frac{20}{360}*2\pi r$ and simplifying a bit,

$8\pi=\frac{2}{36}*2\pi r$ and a bit more,

$8\pi=\frac{4\pi r}{9}$. 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