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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 ?

A3pi radians
B3radians
C3r radians
D3pi r radians

Verified Answer :

nobillionaireNobley

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.

JeanaShupp

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.


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