Areas of circles and sectors

The  exercise appears under the Geometry Math Mission. This exercise introduces the sector area formula in radians and degrees.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the area of the sector: This problem provides a diagram with a circle and the measure of a central angle. The student is expected to find the area of the sector and write it in the space provided.Aocas1.png
 * 2) Find the area of the circle: This problem provides a diagram with a circle, the measure of a central angle, and the are of the sector associated with that central angle. The student is expected to find the total area of the circle and write it in the space provided.Aocas2.png

Strategies
Knowledge of the sector area formula, in both radians and degrees, is encouraged to ensure success on this exercise.
 * 1) The arc length formula in radians is $$s=\frac{1}{2}\theta r^2$$. In degrees it is $$s=\frac{\theta}{360}\pi r^2$$.
 * 2) The formula for arc length is not vital to know. These problems can also be set of with knowledge of circumference ($$A=\pi r^2$$), and the ratio mnemonic "part to whole."
 * 3) In the Find the area of the circle problem, efficiency can be increased if it is possible to quickly recognize what fraction of the circle is being observed.
 * 4) The radius in Find the area of the circle always seems to be an integer.

Real-life Applications

 * 1) The area of a sector can be used in security to determine the amount of space covered by security cameras in stores or other venues.
 * 2) The area of sector can be used to determine the amount of paint needed in artistic projects requiring circles.
 * 3) Problems involving arc length and sector area are common on standardized tests, such as the ACT and SAT.