For a partial circle with a central angle of 1/8 * 2π radians, the arc length is πr/4.
The formula for arc length, s, on a circle is given by s = θ * r, where s is the arc length, θ is the central angle in radians, and r is the radius of the circle.
In this case, the central angle, θ, is given as 1/8 * 2π radians, and the radius is denoted by r.
1. Substitute the values:
θ = 1/8 * 2π and s = θ * r = πr/4.
2. Simplify the expression:
The arc length s is equal to πr/4.
The arc length of the partial circle is πr/4.
This result implies that if you know the central angle in radians and the radius of a circle, you can calculate the arc length using the formula πr/4. In this specific case, the fraction 1/8 of the full circle's circumference is represented by the arc length πr/4.