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?

Question

asked Feb 18, 2020 17.7k views

2 Answers

Shashank Bhatt · Answer 1 · 2020-02-22T09:31:19+0000

Answer:
$arc\ length=3$

Explanation:

The formula for calculate the arc lenght is:

$arc\ length=2\pi r((\theta)/(360))$

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:

$arc\ length=C((\theta)/(360))$

Where "C" is the circumference of the circle.

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

$arc\ length=36((30\°)/(360))=3$