172. The length of an arc is 18 cm and the radius of the circle is 6 cm . What is the radian measure of the central angle?

Question

UpStudy AI · Accepted Answer

To find the radian measure of the central angle given the arc length and the radius of the circle, you can use the formula:

$$
\text{Arc Length} (s) = \text{Radius} (r) \times \text{Central Angle} (\theta)
$$

**Given:**
- Arc Length, $$ s = 18 $$ cm
- Radius, $$ r = 6 $$ cm

**Formula:**
$$
\theta = \frac{s}{r}
$$

**Calculation:**
$$
\theta = \frac{18 \text{ cm}}{6 \text{ cm}} = 3 \text{ radians}
$$

**Answer:**  
The radian measure of the central angle is **3 radians**.
The radian measure of the central angle is 3 radians.

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