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To find the arc length of the partial circle, we can use the formula for the arc length \( S \) of a circle, which is given by:

\[
S = r \theta
\]

Where:
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle in radians.

From the image:
- The radius \( r = 1 \), as indicated.
- The angle shown is a quarter of a full circle, which is \( \frac{\pi}{2} \) radians (since a full circle has an angle of \( 2\pi \) radians).

Now, using the formula:

\[
S = 1 \times \frac{\pi}{2} = \frac{\pi}{2}
\]

Thus, the exact arc length is:

\[
\frac{\pi}{2}
\]

If you need the decimal value using \( \pi \approx 3.14 \):

\[
S = \frac{3.14}{2} = 1.57
\]

So the arc length is approximately \( 1.57 \) units.

Would you like more details on any part of this process?

Here are five related questions for you to explore:
1. How do you find the arc length for an arbitrary angle \( \theta \) in degrees?
2. What is the relationship between the radius and the circumference of a full circle?
3. How would the arc length change if the radius were doubled?
4. What is the formula for the area of the sector corresponding to this arc?
5. Can you derive the formula for arc length from the definition of a radian?

**Tip:** Always make sure that the angle \( \theta \) is in radians when using the arc length formula \( S = r\theta \). If the angle is in degrees, convert it by multiplying by \( \frac{\pi}{180} \).

Find the arc length of the partial circle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

Learn how to find the arc length of a quarter circle with a radius of 1. This solution covers the arc length formula S = rθ, using both exact values in terms of π and decimal approximations. Suitable for students in Grades 7-9.

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