The formula for the length of an arc, $L$, intersected by a central angle $\theta$ in a circle with radius $r$, is:

$L = r \cdot \theta$

Where:

• $L$ is the length of the arc,
• $r$ is the radius of the circle,
• $\theta$ is the central angle in radians.

Given:

• $r = 4.5$ cm,
• $\theta = \frac{\pi}{2}$ radians (which equals $1.57$ when $\pi = 3.14$).

Now, calculate the arc length:

$L = 4.5 \cdot 1.57$

$L \approx 7.065 \, \text{cm}$

Rounding to the nearest tenth:

$L \approx 7.1 \, \text{cm}$

So, the arc length is approximately 7.1 cm.

Would you like further details or have any questions?

Here are some related questions you might find interesting:

1. How would the arc length change if the central angle were doubled?
2. How do you find the circumference of a circle using its radius?
3. What is the area of a circle with a radius of 4.5 cm?
4. If the angle is in degrees instead of radians, how do you calculate the arc length?
5. How can you find the radius if the arc length and angle are known?

Tip: Remember, the arc length is directly proportional to both the radius and the central angle.