Common Core Geometry, June 2015, Questions 29
29. In the diagram below of circle O, the area of the shaded sector AOC is 12*pi in2and the length of OA is 6 inches. Determine and state m<AOC.
As shown in the illustration below, the ratio of the area of the sector of a circle to the whole circle is proportional to the measure of the central angle to 360 degrees.
In other words, whatever fraction of the area is shaded in, multiply that same fraction times 360 degrees to get the measure of the central angle of the sector.
Since area is pi*r2, the area of the circle is (6)2pi or 36pi. The sector is 12pi. (12 pi) / (36 pi) = 1/3. The shaded sector is 1/3 of the circle.
Multiply 1/3 times 360, and the central angle is 120 degrees.
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