A sector is a portion of a circle. There is a relationship between the central angle that creates the sector, the area of the sector, and the area of the circle. In this section of the lesson, you will investigate that relationship.
Use the dynamic geometry sketch below in order to complete the table that follows. To do so, use a circle with a radius of 3 units. To fill in the table, you may copy it into your notes. Use the information in the table to answer the conclusion questions that follow.
Click and drag the Radius slider to change the radius of the circle. Click and drag the Angle slider to change the measure of the central angle.
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The two ratios are approximately equal.Interactive popup. Assistance may be required.
Yes, the relationship is proportional because the two ratios are equal.Interactive popup. Assistance may be required.
Measure of Central Angle over 360 Measure of Central Angle 360 = Area of Sector over Area of Circle Area of Sector Area of CircleDoes the relationship between the measure of the central angle, the area of the sector, and the area of the circle change if the radius of the circle changes? Why or why not?
Rewrite your proportion in the form of an equation that you can use to calculate the area of the sector.
Use the relationship from this section to answer the following questions.
If the fountain has a diameter of 9 yards, what is the area of the sector BAC shown in green?
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Draw a picture to help you. The formula for the circumference of a circle is C = 2π r, and you can use the radius from this formula to calculate the area of the circle.