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Answer :
To find the length of the arc intersected by a central angle in a circle, we can use the formula for arc length. The formula is:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here are the steps to solve the problem:
1. Identify the radius of the circle:
The radius [tex]\( r \)[/tex] of the circle is given as 10 inches.
2. Identify the central angle:
The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Substitute the radius and the central angle into the arc length formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3} \][/tex]
5. Calculate the numerical value (if needed, use [tex]\(\pi \approx 3.14\)[/tex] for approximation):
[tex]\[ \text{Arc Length} ≈ \frac{20 \times 3.14}{3} ≈ 20.94 \text{ inches} \][/tex]
Hence, the approximate length of the arc is [tex]\( 20.94 \)[/tex] inches.
Therefore, the correct answer is:
[tex]\[ \boxed{20.94 \text{ inches}} \][/tex]
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here are the steps to solve the problem:
1. Identify the radius of the circle:
The radius [tex]\( r \)[/tex] of the circle is given as 10 inches.
2. Identify the central angle:
The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Substitute the radius and the central angle into the arc length formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3} \][/tex]
5. Calculate the numerical value (if needed, use [tex]\(\pi \approx 3.14\)[/tex] for approximation):
[tex]\[ \text{Arc Length} ≈ \frac{20 \times 3.14}{3} ≈ 20.94 \text{ inches} \][/tex]
Hence, the approximate length of the arc is [tex]\( 20.94 \)[/tex] inches.
Therefore, the correct answer is:
[tex]\[ \boxed{20.94 \text{ inches}} \][/tex]
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