40.9k views
4 votes
An arc with length 5 pi over 4 inches is formed by a 15 degree central angle what is the radius of the circle

1 Answer

4 votes

Answer:

Radius of the circle is 15 inches.

Explanation:

Relation between length of arc, radius and the angle subtended by the arc on center is:


\theta = (l)/(r) ..... (1)

where
\theta is the central angle in radians subtended by arc


l is the length of arc


r is the radius of arc

We are Given the following details:


l = (5\pi)/(4)\ inch


\theta = 15^\circ

We know that
\pi \ radians = 180 ^\circ

Converting
\theta to radians:


\theta =(\pi)/(180) * 15 radians

Putting the values of
\theta and
l to find the value of
r


(\pi)/(180) * 15 = (5\pi)/(4r)\\\Rightarrow r = (45)/(3) \\\Rightarrow r = 15 \ inches

Hence, Radius of the circle is 15 inches.

User RVG
by
3.5k points