Question

A circle has a radius f length r. If you mark off an arc on the circle of length 3r, what is the measurement of the angle that subtends the arc ?

A. 3pi radians
B. 3radians
C. 3r radians
D. 3pi r radians

Answer 1

Length of an arc = θ/2π * 2πr = rθ; where θ is the angle substended by the arc at the center.
3r = rθ
θ = 3 radians.

Answer 2

Answer: B. 3radians

Step-by-step explanation:

Given: Radius of a circle = r

Length of a arc = 3r

To find the measurement of the angle that subtends the arc ($\theta$)

We know that the length of the arc $(l)=\theta\times\ r$

$\Rightarrow\theta=\frac{l}{r}\\\\\Rightarrow\theta=\frac{3r}{r}\\\\\Rightarrow\ \theta=3\ radians$

Hence, the measurement of the angle that subtends the arc = 3 radians.