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March 29, 2017

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Hello, I have this question to which it's solution I'm not quite sure of. The question is based on a diagram, and I can't really present it but I'll explain it to my very best, thank you very much for trying to understand my bad presentation of the question.

The diagram is a circle, with center O and points A and B lying on the circle. Radius is 6cm therefore OA=OB=6cm, such that angle AOB = 79 degrees.
Find the area of the shaded segment of the circle contained between the arc AB and the chord [AB].

The solution was a simple sentence, [ (79degrees/360 degrees) x pi x 6^2 ] - [(1/2)(6)(6)sin79]
I understand that [(1/2)(6)(6)sin79] was derived from the rule 1/2absinc and we're finding the area of the triangle.
Therefore, [ (79degrees/360 degrees) x pi x 6^2 ] must be the area of the sector. However, when I looked up the formula for the area of sector, it's (1/2)(delta)(r)^2, where delta is the angle measured in radians.
Primarily, how did [ (79degrees/360 degrees) x pi x 6^2 ] come about then?

  • Math - ,

    because the [ (79degrees/360 degrees) x pi x 6^2 ] would be the measure of that section of the circle.
    the area of the whole circle would be pi x r^2 but since you're only solving for that section it would be 79/360 times that whole area of the circle to solve for that section.
    Think of a circular pizza and you were asked to find the area of one slice and there are 10 slices, to find the area of one slice you would multiply the area of the whole pizza by (1/10) which represents one slice.
    Hope this helps.

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