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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:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
Where:
- [tex]\( r \)[/tex] is the radius of the circle.
- [tex]\( \theta \)[/tex] is the central angle in radians.
In this problem:
- The radius [tex]\( r \)[/tex] is given as 10 inches.
- The central angle [tex]\( \theta \)[/tex] is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length:
1. Multiply the radius (10 inches) by the central angle [tex]\(\frac{2\pi}{3}\)[/tex]:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
2. First, multiply 10 by 2:
[tex]\[ 10 \times 2 = 20 \][/tex]
3. Next, divide 20 by 3:
[tex]\[ \frac{20}{3} \approx 6.67 \][/tex]
4. Finally, multiply by [tex]\(\pi \approx 3.1416\)[/tex] to get the approximate arc length:
[tex]\[ 6.67 \times 3.1416 \approx 20.94 \][/tex]
Thus, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
Where:
- [tex]\( r \)[/tex] is the radius of the circle.
- [tex]\( \theta \)[/tex] is the central angle in radians.
In this problem:
- The radius [tex]\( r \)[/tex] is given as 10 inches.
- The central angle [tex]\( \theta \)[/tex] is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length:
1. Multiply the radius (10 inches) by the central angle [tex]\(\frac{2\pi}{3}\)[/tex]:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
2. First, multiply 10 by 2:
[tex]\[ 10 \times 2 = 20 \][/tex]
3. Next, divide 20 by 3:
[tex]\[ \frac{20}{3} \approx 6.67 \][/tex]
4. Finally, multiply by [tex]\(\pi \approx 3.1416\)[/tex] to get the approximate arc length:
[tex]\[ 6.67 \times 3.1416 \approx 20.94 \][/tex]
Thus, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
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