A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of StartFraction 2 pi Over 3 EndFraction


To find the length of an arc in a circle, you can use the formula:

\[
\text{Arc length} = r \times \theta
\]

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

Here, the radius \( r = 10 \) inches, and the central angle \( \theta = \frac{2\pi}{3} \) radians.

Now, substitute the values into the formula:

\[
\text{Arc length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\]

To get the approximate length, use \( \pi \approx 3.1416 \):

\[
\text{Arc length} \approx \frac{20 \times 3.1416}{3} \approx 20.944 \text{ inches}
\]

Thus, the approximate length of the arc is **20.944 inches**.

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. What is the area of the sector formed by the same central angle?
2. How does the arc length change if the central angle doubles?
3. What would be the arc length if the radius of the circle was doubled?
4. How do you convert a central angle from degrees to radians?
5. How is the formula for arc length derived?

**Tip:** Remember, the angle must always be in radians when using the arc length formula. If it's in degrees, convert it by multiplying by \( \frac{\pi}{180} \).

A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of StartFraction 2 pi Over 3 EndFraction.

Learn how to calculate the length of an arc in a circle with a radius of 10 inches and a central angle of 2π/3 radians. This geometry problem explains the arc length formula and how to convert radians to degrees, suitable for high school students.

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