Area of a Circular Segment
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2) $m(A\hat{O}B) = 30^\circ$ $|OA| = r = 8\text{ cm}$. Find $T.A. = ?$
This question includes visual content: The image shows a circle with center O. Points A and B lie on the circle's circumference. Radii OA and OB form a central angle of 30 degrees. The region bounded by the chord AB and the arc AB is shaded.
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Hi Suden, let's solve for the shaded area in this circle step by step.
Area of the Shaded Segment
From the problem description and diagram, we know the radius of the circle is eight centimeters, and the central angle of the sector is thirty degrees.
The shaded area is a circular segment. We can find it by taking the area of the entire sector O A B and subtracting the area of triangle O A B.
First, let's calculate the area of the sector. The formula is theta over three hundred sixty degrees times pi r squared.
1. Area of Sector $OAB$
Substituting thirty for theta and eight for r, thirty over three hundred sixty simplifies to one twelfth.
This simplifies to sixty-four pi divided by twelve, which reduces further to sixteen pi over three square centimeters.
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