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

Answer:

Option (1)

Step-by-step explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle = $\frac{360}{3}$ = 120°

From the formula of arc length,

Length of arc = $\frac{\theta}{360}(2\pi r)$

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 = $\frac{120}{360}(2\pi r)$

12 = $\frac{2}{3}\pi r$

$18=\pi r$

r = $\frac{18}{\pi }$

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.