218,530 views
25 votes
25 votes
Find the length of the arc.arc circle 4A. 5400π miB. 125π16 miC. 15π miD. 135π mi

Find the length of the arc.arc circle 4A. 5400π miB. 125π16 miC. 15π miD. 135π mi-example-1
User Evgeniya Manolova
by
2.8k points

1 Answer

17 votes
17 votes

The arc length can be calculated by using the following formula


s=r\emptyset

theta, is the central angle of the arc in radians, and r is the radius

We have been given that the radius is 18, and the central angle is 150 degrees. To find the arc length, let us start by converting the angle to radians. We can do this by multiplying 150 by the ratio between radians and degrees (pi/180). This works because 180 degrees is equal to pi radians (so the fraction is equal to 1):


\begin{gathered} 150*(\pi)/(180) \\ (15\pi)/(18) \\ (5\pi)/(6) \end{gathered}

So, the sector is 5pi/6 radians. Now, we can solve this by multiplying this by the radius of the circle:


(5\pi)/(6)*18=5\pi *3=15\pi

Therefore, the answer is C, or 15pi