Question

A sector of a circular patio intercepts an arc that is 3.1 meters long and has a central angle of 225 degrees. Find the diameter.

Answer 1

To find the diameter of a circular patio with a sector arc length of 3.1 meters and a central angle of 225 degrees, use the formula for arc length in terms of radius and angle (in radians), solve for the radius, and then double it to get the diameter.

Step-by-step explanation:

To find the diameter of a patio where a sector has an arc length of 3.1 meters and a central angle of 225 degrees, we need to use the relationship between the arc length (s), the radius (r), and the central angle (Θ) in degrees,

Step-by-Step Explanation

1. The formula for arc length is s = rθ, where θ is in radians. To convert degrees to radians, we multiply by π/180. Here, θ = 225°, so in radians, θ = 225(π/180) = (5/4)π.
2. Substitute the arc length and the radian angle into the formula to find the radius: 3.1 = r × (5/4)π.
3. Solve for r: r = 3.1 / [(5/4)π], which gives the radius of the sector.
4. To find the diameter, simply double the radius.

This calculation will yield the diameter of the entire circular patio.