Question

If the circumference of a circle is 36, what is the length of an arc of the circle intercepted by a central angle of 30 degrees?

Answer 1

Answer: $arc\ length=3$

Step-by-step explanation:

The formula for calculate the arc lenght is:

$arc\ length=2\pi r(\frac{\theta}{360})$

Where "r" is the radius and "$\theta$" is the central angle of the arc in degrees.

The formula used to find the circumference of a circle is:

 $C=2\pi r$

Where "r" is the radius.

Then, we can observe that the formula for calculate the arc lenght can be rewritten in this form:

$arc\ length=C(\frac{\theta}{360})$

Where "C" is the circumference of the circle.

Finally we need to substitute the central angle and the circumference into $arc\ length=C(\frac{\theta}{360})$. Then the result is this:

$arc\ length=36(\frac{30\°}{360})=3$

Answer 2

Answer:330 degrees

Step-by-step explanation: It helps by drawing a picture, hope this helps