Question

22. The circumference of the circle below is

108 meters. If the interior angle n is 60°,
what is the length in meters of arc AB?
F) 5
G) 9
H) 11
J) 12
K) 18

Answer 1

The length of arc of circle with interior angle 60° is 18 meter

Explanation:

Given as :

The circumference of circle = C = 108 meters

The interior angle at center of circle = 60°

Let The length of arc = L

So ,

Length of arc = L =
`(\Pi * radius* \Theta )/(180^(\circ))`

∵ circumference of circle =
`2* \Pi * radius`

Or, 108 =
`2* \Pi * radius`

∴ r =
`(108)/(2\pi )`

So, Length of arc =
`((\Pi * \Theta )/(180)) * ((108)/(2* \Pi ))`

Or, L =
`((\Pi * \60 )/(180)) * ((108)/(2* \Pi ))`

Or, L =
`(36)/(2)` = 18 m

Hence The length of arc of circle with interior angle 60° is 18 meter Answer