# The radius of a given circle is 11 cm. Find the central angle (measured in radians) of a sector of the circle whose area is 250 cm2. ?

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• Area is (1/2)r²θ....where r is the radius and θ is the central angle in radians.

so, (1/2)(11)²θ = 250

i.e. θ = 500/121 => 4.13 radians

:)>

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• The radius of a given circle is 11 cm.

Find the central angle (measured in radians) of a sector of the circle whose area is 250 cm^2.

C = 2 pi 11

and

A = 121 pi = 380.132711 cm^2

The central angle:

250/380 (2 Pi) = 4.13367454 radians

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• The formula for the area of a sector is:

A = ½ r² θ

A : area (250 cm²)

θ : central angle of the sector (in radians)

250 = ½ (11²) θ

500 = 121 θ

θ = 500/121

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• area of the circle is πr² = π11² = 121π cm²

the sector is what percent of that

As = 250/121π cm²

that percent is the same percent of 2π radians, the full circle

angle = 2π(250/121π) = 500/121 = 4.13 rad

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