To find the arc length of the partial circle, we'll use the formula for the arc length of a circle:

$\text{Arc Length} = \theta \times r$

Where:

• $\theta$ is the central angle in radians.
• $r$ is the radius of the circle.

Step 1: Find the central angle $\theta$

Since $\frac{1}{4}$ of the circle is cut off, the central angle $\theta$ corresponds to a quarter of the full circle. The total angle in a circle is $2\pi$ radians.

$\theta = \frac{2\pi}{4} = \frac{\pi}{2} \text{ radians}$

Step 2: Use the radius $r = 5$ to find the arc length

Now, plug the values into the formula:

$\text{Arc Length} = \frac{\pi}{2} \times 5 = \frac{5\pi}{2} \text{ units}$

So, the arc length of the partial circle is $\frac{5\pi}{2}$ units, which is approximately 7.85 units.

Would you like more details or have any questions? Here are five related questions to consider:

1. How would the arc length change if half the circle were cut off?
2. How do you convert radians to degrees?
3. What is the relationship between the circumference of a circle and its arc length?
4. How would you find the area of the sector corresponding to the $\frac{1}{4}$ circle cut off?
5. If the radius were doubled, what would the new arc length be for the same central angle?

Tip: Remember, the arc length formula $\theta \times r$ only works when $\theta$ is in radians. Always convert degrees to radians if necessary.