Question

question 6 points 4 find the arc length of the circle whose radius is 10 cm and whose central angle is 120°. use π = 3.14

Explanation:

Step1: Recall arc length formula

The formula for the arc length \( L \) of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( L=\frac{\theta}{360^{\circ}}\times2\pi r \).

Step2: Substitute the given values

Given \( r = 10\) cm, \( \theta=120^{\circ} \), and \( \pi = 3.14 \). Substitute these into the formula:
\( L=\frac{120^{\circ}}{360^{\circ}}\times2\times3.14\times10 \)
First, simplify \( \frac{120^{\circ}}{360^{\circ}}=\frac{1}{3} \).
Then, calculate \( 2\times3.14\times10 = 62.8 \).
Now, multiply \( \frac{1}{3}\times62.8\approx20.93 \) (rounded to two decimal places).

Answer:

The arc length is approximately \( 20.93 \) cm.