Question in image

Question

Answer 1

First find the circumference. The circumference is 2π(3) = 6π

The circumference is the arc length of the entire 360° of a circle.

We however just want the arc length within that 100° angle.

Thus the arc length is 100/360 of the entire circumference

So just do 6π * (100/360)

Answer 2

Since the radius of the circle is 3, the entire circumference is 2*pi*r = 6*pi

The key concept is that, for example, if your angle "sweeps" out half the total angle measure (360), then it would sweep out half of the total circumference. If it sweeps out a third of the total angle measure, it sweeps out a third of the circumference, etc.

This angle sweeps out a fraction of (100/360) of the total measure, and thus sweeps out the same fraction of the circumerference:

(100/360)*(6*pi) ≈ 5.23599