Area of a Sectors of a Circle
Deriving Area of a Sector of a Circle
Objectives:
Derive a formula for area of a sector.
Use the formula to find area of a sector.
Use the formula in real world applications.
Your mission is to come up with a formula for area of a sector of a circle using the central angle of the sector.
Directions: Measure the radius (cm) of your cookie and find the area of the entire cookie (Area= πr^2). Check your answer with the GeoGebra Cookie Applet.
Cut your cookie in half. Eat one half of the cookie. What is the area of ½ of the cookie? Check your answer with the GeoGebra Cookie Applet by selecting "Sector"
What is the measure of the central angle for half of the cookie?
Cut half of your cookie in half. What part of the entire cookie is this? What is the area of this sector (define)?
What is the measure of the central angle for this ¼ part of the cookie?
How can we use the central angle in a fraction that would help us get 1, ½ , ¼, … ?