My Math Forum Finding area of shaded segment within a circle.

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 May 8th, 2012, 06:34 AM #1 Member   Joined: Apr 2012 Posts: 92 Thanks: 0 Finding area of shaded segment within a circle. 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?
May 8th, 2012, 07:02 AM   #2
Math Team

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Re: Finding area of shaded segment within a circle.

Quote:
 Originally Posted by Tutu 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].
Hint: could be worded:
The diagram is a semi-circle, with center O and points A and B lying on the semi-circle's circumference.
Or even this way (since 79 < 90):
The diagram is a quarter-circle, with center O and points A and B lying on the quarter-circle's circumference.

 May 8th, 2012, 07:11 AM #3 Member   Joined: Apr 2012 Posts: 90 Thanks: 0 Re: Finding area of shaded segment within a circle. Hahaa yeah thanks! Sorry, I'm not good at phrasing.
May 8th, 2012, 07:14 AM   #4
Math Team

Joined: Oct 2011

Posts: 14,597
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Re: Finding area of shaded segment within a circle.

Quote:
 Originally Posted by Ter Hahaa yeah thanks! Sorry, I'm not good at phrasing.
You just had a name change: Tutu to Ter ?

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# formula for area of a shaded portion

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