Question

Find the length of the arc of a circle whose radius is 6 and whose central angle is 10 degrees
Find the length of the arc of a circle whose radius is 6 and whose central angle is 10 degrees
@Mathematics

Answer 1

\[s = r \theta\] where theta is in radians. Since you have degrees you have to turn it into radians. So to do that you do this \[10 * \frac{\pi}{180}\] or \[\frac{\pi}{18}\] Now all you do is plug in the values \[s = (6)(\frac{\pi}{18})\] Which simplifies down to \[s = \frac{\pi}{3}\] If you want a decimal number then just plug pi/3 in a calculator.

Answer 2

Or you can set up a ratio.
Arc distance(s):Circumference(C):: 10 degrees:360 degrees
s:C::10:360 C=2piR=12pi
360s=120pi
s=(120/360)pi
s=(1/3) pi or pi/3