Question

A circle has a radius of length r. If you mark off an arc on the circle of length 3r. What is the measurment of of the angkebthat sub tends the arc?
A.3 radians
B. 3piR radians
C. 3r radians
D. 3pi radians

Answer 1

Answer:

A. 3 radians.

Step-by-step explanation:

A circle arc is a portion of a circle. And the formula of the length of arc with the angle in radians is:

$S=R.\beta$, where:

$S:$ The arc length.

$R:$Radius of the circle.

$\beta :$Angle in radians.

Then we know that the radius of the circle is $R=r$, and the arc length is $S=3r$. Then using the arc length formula, the angle that subtends the arc is:

$\beta =\frac{S}{R}$

$\beta =\frac{3r}{r} \\\beta =3 radians$

Then the correct option is letter A.

Answer 2

The appropriate choice is ...
  A. 3 radians

_____
Arc length (s) is given in terms of radius (r) and central angle (θ) in radians by the formula
  s = rθ

When you substitute your given information, you have
  3r = rθ
Dividing by r gives
  θ = 3 . . . . . . . radians