Question

Find the radius r of the circle if an arc of length 6 m on the circle subtends a central angle of 3π/7 rad. (Round your answer to two decimal places.) r=×m

Answer 1

The radius of the circle, rounded to two decimal places, is 4.46 meters. This is found by rearranging the formula for arc length to solve for radius, and substituting in the given values.

Step-by-step explanation:

To find the radius of a circle from the arc length and the central angle, you can use the formula for the arc length, which is: L = r * θ, where L is the arc length, r is the radius of the circle and θ is the central angle in radians.

In this particular case, the arc length (L) is 6 meters and the central angle (θ) in radians is 3π/7 rad. To find the radius (r), we can rearrange the formula to r = L / θ.

Substituting in the given values gives r = 6 / (3π/7) = 14/π meters.

So, rounded to two decimal places, the radius of the circle is about 4.46 meters.

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