Question

Find the arc-length of the sector of a circle with the given radius r and central angle θ. Give the answer in the given unit of measure, rounded to the nearest hundredth. r=9m;θ=π3

Answer 1

The arc-length of the sector of a circle with a radius of 9m and a central angle of π/3 radians is approximately 9.42 meters.

Step-by-step explanation:

The student asked to find the arc-length of a sector of a circle with the radius (r) of 9 meters and a central angle (θ) of π/3 radians. To calculate the arc-length (As), one can use the formula:

As = r * θ.

Here, r = 9m and θ = π/3. Plugging these values into the formula, we get:

As = 9m * π/3 = 3π meters.

To give the answer rounded to the nearest hundredth, we calculate 3π which is approximately 9.42 meters.

So, the arc-length of the sector is approximately 9.42 meters.