The length of the darkened arc in terms of π is: D. 15π in.
In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Length of an arc = 2πr × θ/360
Where:
- r represents the radius of a circle.
- θ represents the angle subtended by the arc.
Substituting the given points into the length of an arc formula, we have the following;
Length of an arc = 2π × 9 × 300/360
Length of an arc = 2π × 9 × 5/6
Length of an arc = π × 3 × 5
Length of an arc = 15π in.
