Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS?

What is the approximate circumference of the circle?

cm

What is the approximate length of arc RS?

cm

There are a total of 360° in any given circle, so an arc swept out by 60° of that 360° would make up 60/360 = 1/6 of the circle's circumference.

The formal for the circumference of a circle comes out of the definition of one of the most famous constants in mathematics: π. π is defined as the ratio between a circle's circumference and its diameter, or:

From this definition, we can multiply both sides of the equation by d to obtain

or, circumference is π times the diameter. To find the diameter, we just need to double the radius, giving us 5 * 2 = 10cm. Usually you'll see π approximated as 3.14, which is likely what they want you to use here. Using that approximation, we find the circumference to be 3.14 * 10 = 31.4 cm.

Finally, to get the length of that arc, we just need to take 1/6 of the circumference (since the arc sweeps out 1/6 of the circle), giving us 31.4 * 1/6 ≈ 5.2 cm.