Question

rounded to the nearest whole, what is the radius length if minor arcYZ = 12 and angleYXZ is one-third of a full circle? (i guessed it idk if it’s right)

Answer 1

Option (1)

Explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle =
`(360)/(3)` = 120°

From the formula of arc length,

Length of arc =
`(\theta)/(360)(2\pi r)`

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 =
`(120)/(360)(2\pi r)`

12 =
`(2)/(3)\pi r`

`18=\pi r`

r =
`(18)/(\pi )`

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.