Question

Find the arc length of a central angle of pi/6 in a circle whose radius is 10 inches.

Answer 1

Answer: 5.23 inches

Explanation:

Let the length of the arc intersected by a central angle x be l.

Given:- Central angle
`x=(\pi)/(6)\text{ radians}`

Radius r= 10 inches

We know that ,

`l=x\ r\\\\\Rightarrow\ l=(\pi)/(6)*10\\\\\Rightarrow\ l=(3.14*10)/(6)= 5.2333333333\approx5.23\text{ inches}`

Thus, the length of the arc of a central angle
`(\pi)/(6)\text{ radians}` is 5.23 inches.

Answer 2

= 5/3 * pi inches

or approximately 5.235987756 inches

Explanation:

The formula for arc length = r * theta where theta is in radians

arc length = 10 * pi/6

= 10/6 * pi

= 5/3 * pi

or approximately 5.235987756 inches