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Answer :
To find the length of an arc in a circle, you can use the formula:
[tex]\[
\text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)}
\][/tex]
Here’s how to apply this formula to the problem:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The central angle ([tex]\(\theta\)[/tex]) is given in radians as [tex]\(\frac{2\pi}{3}\)[/tex].
2. Apply the Formula:
- Substitute the given values into the formula for arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the Arc Length:
- Multiply the radius by the angle in radians:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
[tex]\[
\text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)}
\][/tex]
Here’s how to apply this formula to the problem:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The central angle ([tex]\(\theta\)[/tex]) is given in radians as [tex]\(\frac{2\pi}{3}\)[/tex].
2. Apply the Formula:
- Substitute the given values into the formula for arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the Arc Length:
- Multiply the radius by the angle in radians:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
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Rewritten by : Jeany
