Math Tip of the Day: Circle Sector Area

Last week, we discussed one concept of circles:  arc length.  This week’s math tip will be on sector area of circles.  A sector is a section of a circle.  Like a piece of pie or a slice of pizza!  And the sector area is the area of that particular section.   To calculate the sector area, you can set up a proportion as we did for the arc length (see diagram and example below).

Area of a Sector


Similar to the arc length, the ratio of the sector area and the area is proportional to the ratio of the central angle measure and the total degrees of the circle.  Keep in mind that the sector area is part of the entire area, and the central angle measure is a part of the total degrees.  So that makes it all proportional.  Just like when we calculated for the arc length.

Back to the example.  First, substitute the values for C and r (C= central angle measure, r = radius).  Then multiply the values in the denominator of the first ratio.  Cross multiply and divide, and you have your answer!

Calculate the area for a slice of round cake if the radius is 4 inches and the central angle is 45 degrees.