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Answer :
To find the length of the arc intersected by a central angle in a circle, we use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here, we're given:
- The radius of the circle is [tex]\( 10 \)[/tex] inches.
- The central angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
Let's plug these values into the formula:
1. Identify the Radius:
The radius of the circle is [tex]\( 10 \)[/tex] inches.
2. Identify the Central Angle in Radians:
The central angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
3. Calculate the Arc Length:
Using the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Simplify and Calculate:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
5. Approximate the Arc Length:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc intersected by a central angle of [tex]\( \frac{2\pi}{3} \)[/tex] is [tex]\( 20.94 \)[/tex] inches. The correct option is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here, we're given:
- The radius of the circle is [tex]\( 10 \)[/tex] inches.
- The central angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
Let's plug these values into the formula:
1. Identify the Radius:
The radius of the circle is [tex]\( 10 \)[/tex] inches.
2. Identify the Central Angle in Radians:
The central angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
3. Calculate the Arc Length:
Using the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Simplify and Calculate:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
5. Approximate the Arc Length:
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc intersected by a central angle of [tex]\( \frac{2\pi}{3} \)[/tex] is [tex]\( 20.94 \)[/tex] inches. The correct option is 20.94 inches.
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