Question

Find the arc-length of the sector of a circle with the given radius r and central angle 0. Give the answer in the given unit of measure, rounded to the nearest hundredth.r = 25 m; θ = 12π/7

Answer 1

Given a radius and a central angle in radian, the formula in solving arc length is:

`AB=\theta* r`

Since the angle and radius are given already in the problem, let's plug it in to the formula above.

`AB=(12\pi)/(7)(25m)`

Then, solve.

`AB=(300\pi m)/(7)=(942.47779m)/(7)\approx134.64m`

Therefore, the length of an arc having a central angle of 12π/7 is approximately 134.64 meters.