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A circle has a radius of 25 centimeters and a central angle EOG that measures 100 degrees. What is the area of sector EOG? Use 3.14 for pi and round your answer to the nearest tenth. A) 2180.6 cm2 B) 21.8 cm2 C)43.6 cm2 D) 545.1 cm2

Verified Answer :

Giovi

I found C) 43.6 cm^2
I used the fact that the area is equal to radius*angle
But the angle has to be in radians (NOT degrees!)
I change the angle into radians using the proportion
\(\pi :180^{o} = x : 100^{o}\)
and I got x=\(\frac{100* \pi }{180} = \frac{5}{9} \pi\) rad
So:
Area=\(25* \frac{5}{9}*3.14=43.6 cm^{2}\)

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