Arc Length and Sector Area

A sector is part of a circle, and so to calculate the arc length of a sector and the area of a sector, we take the relevant circle’s circumference or area and multiply it by the proportion of the circle we have. To find the proportion we take the number of degrees in our sector and divide by 360º (which is the number of degrees in a whole circle). As always, we can also work backwards to find the angle or the radius.

Examples

Exercise

Let’s complete exercise 18 from pages 25 and 26 of the core textbook:

The answers are below: