Find the arc length of a circle whose central angle is 90 degrees and radius of 10.

The formula to find the arc length \( s \) of a circle is:

\[
s = r \theta
\]

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

First, convert the given angle from degrees to radians:
\[
\theta = \frac{90^\circ \times \pi}{180^\circ} = \frac{\pi}{2} \text{ radians}
\]

Now, plug in the values:
\[
s = 10 \times \frac{\pi}{2} = 5\pi
\]

Thus, the arc length is:
\[
s = 5\pi \approx 15.71 \text{ units}
\]

Would you like any more details, or do you have any questions?

Here are 5 related questions to consider:
1. How would the arc length change if the angle were 180 degrees?
2. How do you find the circumference of a full circle?
3. What happens to the arc length if the radius is doubled?
4. How do you convert radians to degrees?
5. What is the arc length of a semicircle with radius 7 units?

**Tip:** Always ensure the angle is in radians when using the formula \( s = r \theta \).

Learn how to find the arc length of a circle with a central angle of 90 degrees and a radius of 10 units. This problem covers key geometric concepts like radians and arc length, with step-by-step guidance on using the arc length formula. Suitable for students in Grades 9-12.

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