Example Problems

Some examples:

In the circle below, if x is 120, what fraction of the area of the circle is the area of the shaded region?

Looking at our equality above, we can see that 


In this case, the area of the shaded region (sector) is one third the area of the entire circle.

In the circle below, if x is 110, minor arc MN is what fraction of the circle?

Going back to our equalities, we know the central angle, so we can plug that in.


One more example:

In the circle below, if minor arc MN = (frac{2pi}5) , what fraction of the circle is arc MN?

When we see (pi) in our problem, we know we’re dealing with radians.  The formulas stay the same; we just have to remember it is (2π) all the way around the circle rather than 360°.