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Find the area of circle Y. The image is represented by circle Y with a sector XYZ that has an area of 85.5 square meters. That sector has an arc that measures 117 degrees. The radius of the circle is unknown.

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sqdancefan

Answer:

  263.08 m²

Step-by-step explanation:

The fraction of circle area that a sector represents is proportional to the central angle.

Proportion

  circle area/circle angle = sector area/sector angle

  circle area / 360° = 85.5 m² / 117°

Multiplying by 360°, we have ...

  circle area = (360/117)(85.5 m²) = 263.08 m²

The area of the circle is about 263.08 m².

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