SOLUTION: In the circle, the area of sector OAB is 4/3 π cm². The area of the shaded region, in cm² , is? Image to problem: https://ibb.co/RHyYDdF Thanks!

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Question 1198840: In the circle, the area of sector OAB is 4/3 π cm². The area of the shaded region, in cm² , is?
Image to problem:
https://ibb.co/RHyYDdF
Thanks!
Answer by greenestamps(13200) About Me  (Show Source):
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The area of sector OAB is (4/3)pi cm^2.

Angle AOB is 120 degrees, so the sector is 1/3 of the circle.

So the area of the whole circle is 4pi cm^2; so the radius of the circle is 2 cm.

Triangles ADC and BDO are congruent, so the shaded area is the same as the area of sector COB.

The area of sector COB is half the area of sector OAB, which is given as being (4/3)pi cm^2.

ANSWER: (2/3)pi cm^2