334,846 views
21 votes
21 votes
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.

User Span
by
2.9k points

1 Answer

11 votes
11 votes

Answer:

263.08 m²

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.

User Akrohit
by
3.2k points