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A circle has a sector with area (69/5)π and central angle 138∘. What is the area of the circle? (Give an exact answer. You answer may include pi. Example: 3/2 pi or 3pi/2 or 6pi.)

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nobrains

Answer:

36π

Step-by-step explanation:

A circle has 360°.

The given section of the circle has 138°, which is 138/360 of the area of the entire circle. Let A be the area of the entire circle.

[tex]\frac{138}{360}A = \frac{69}{5}\pi \\A = \frac{69}{5 }\pi \frac{360}{138} = 36\pi[/tex]

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