# The area of the circle is 9. Find the area of the sector of this circle with a central angle of 80 degrees.

October 16, 2021 | education

| The area of a circular sector resting on an arc with a degree measure α is calculated by the formula:

Ssect = (πR ^ 2 * α) / 360,

where πR ^ 2 is the area of the entire circle, α is the degree measure of the arc on which the circular sector rests.

By hypothesis, R ^ 2 = 9.

The center angle of the circular sector is 80 degrees. It is known that the degree measure of the central angle is equal to the degree measure of the arc on which it rests, then the degree measure of the arc on which the circular sector rests is equal to 80 degrees. Thus:

Ssect = (9 * 80) / 360 = 720/360 = 2.

Answer: Sect = 2.

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