how many meters in length is the radius of the circle?

Question

If a central angle of measure 30° is subtended by a circular arc of length 6 meters, as
is illustrated below, how many meters in length is the radius of the circle?

 

 

A. 36/π
B. 15
C. π
D. 36/π
E. 180

Answer 1

Parviz is correct.

 

 

Another way to work the problem:

 

30 degrees is 1/12 of the total degrees in a circle:  30/360 = 1/12

 

Therefore, it should cut off 1/12 of the circumference.

 

6 = 1/12 C

 

Multiply both sides by 12 to get the circumference:

 

6*12 = 12(1/12)C

72 = C

 

Since C = 2(pi)(r):

 

72 = 2(pi)(r)

 

Divide both sides by 2(pi)

 

72/(2)(pi) = r

 

r = 36/pi

 

 

Answer 2

πr = 180

 

πr/6 = 30 = 6

 

  r = 36/Π      D is the correct answer