Answer:
It can sometimes be equal to π. However, it is equal to our central angle.
Step-by-step explanation:
First, recall that arc length is given by:
[tex]s=r\theta[/tex]
Where s is the arc length, r is the radius, and θ is the central angle of the arc in radians.
So, the ratio of the arc length to the radius is:
[tex]\displaystyle \frac{r\theta}{r}[/tex]
The radius r cancels. Hence, we are left with:
[tex]=\theta[/tex]
So, the ratio of the arc length to the radius does not equal π (although it can sometimes if the central angle is π radians (or 180°)). Rather, the ratio is equivalent to the central angle.
So, for example, if we have a circle with radius 7 with a central angle of 3π/2 (this gives us an arc length of 21π/2), then the ratio of the arc length to the radius will be 3π/2 (our central angle).
