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3 years ago

12

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 angkebtha

t sub tends the arc?
A.3 radians
B. 3piR radians
C. 3r radians
D. 3pi radians

2 answers:

MrMuchimi3 years ago

4 0

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.

katrin2010 [14]3 years ago

3 0

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

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