Question

1. what is the length of the arc qr?

image of a circle with center p, radius 10 cm, angle ∠qpr = 120°, points q, r, s on the circle
options:

• $\frac{5}{3}pi$
• $\frac{1}{3}pi$
• $\frac{10}{3}pi$
• $\frac{20}{3}pi$

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify given values

Here, the radius \( r = 10 \, \text{cm} \) and the central angle \( \theta = 120^\circ \).

Step3: Substitute values into the formula

\[

$$\begin{align*} L &= \frac{120^\circ}{360^\circ} \times 2\pi \times 10 \\ &= \frac{1}{3} \times 20\pi \\ &= \frac{20}{3}\pi \end{align*}$$

\]

Answer:

\(\frac{20}{3}\pi\) (corresponding to the option with \(\frac{20}{3}\pi\))