Arc length of a sector

Question

On a circle of radius 5m, what is the arc length of a sector whose central angle is 7 Pi / 6?

Answer 1

Here's a way to think about this that might be helpful.

A sector with a central angle of 2π radians corresponds to the whole circle.

For a the circle of radius (r), we know that the circumference is 2πr.

So we get the arc length of a sector with a central angle of 2π radians by multiplying by the radius (r).

If r = 5 m, then the circumference is 10π m ≈ 31.4 m

We get the arc length of a sector with any central angle measure by multiplying by the radius (r).

So if we have a sector whose central angle is 7π/6, its arc length is 7πr/6.

If the radius of the circle is 5 m, then the arc length is 7π(5)/6 = 35π/6 m ≈ 18.3 m.

Answer 2

If a circle has a radius of 5 m, then its circumference is 2π(5) or 10π meters.

A central angle of 7π/6 is a fraction of the entire circle which has a central angle of 2π.

What fraction of 2π is 7π/6?

That would be (7π/6) / 2π = 7/12

So the arc length intercepted by the sector is 7/12 of the entire circumference: 7/12 (10π) = 35π/6 meters.

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Answer 3

(7π/6)(5) = ?