Three friends are sharing a inch pizza equally. Emily is becoming a nutritionist and is curious about how many calories are in a slice. To find out, she will calculate the area of one slice.
From the fact that equals an equivalent formula can be written if the central angle is given in radians.
Since the measure of an arc is equal to the measure of its central angle, the arc measures Therefore, by substituting for another version of the formula is obtained which can also be written in degrees or radians.
Consider sector bounded by and
Recall that the area of a circle is By substituting it into the equation and solving for the area of a sector, the desired formula can be obtained. Therefore, the area of a sector of a circle can be found by using the following formula.
Like the pizza problem, numerous real-life problems can be modeled by sectors of a circle.
Tiffaniqua knows that measures
Consider a two-dimensional image of Pac-Man. The area covered by Pac-Man is about square millimeters.
In his free time, Dylan enjoys making decorative figures by hand. He has identical sectors and brings these sectors together as shown.
Dylan knows that the area of each sector is square millimeters.
From the diagram, it can be seen that the region bounded by and is a sector of