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Answer :
To find the approximate length of the arc intersected by a central angle in a circle, we can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
In this problem, you're given:
- The radius of the circle, which is 10 inches.
- The central angle, given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, we can plug these values into the formula:
1. Radius = 10 inches
2. Central Angle = [tex]\(\frac{2\pi}{3}\)[/tex] radians
Using the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
When you multiply these values:
[tex]\[ \text{Arc Length} ≈ 20.94 \text{ inches} \][/tex]
So, the approximate length of the arc is 20.94 inches, which corresponds to the option "20.94 inches".
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
In this problem, you're given:
- The radius of the circle, which is 10 inches.
- The central angle, given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, we can plug these values into the formula:
1. Radius = 10 inches
2. Central Angle = [tex]\(\frac{2\pi}{3}\)[/tex] radians
Using the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
When you multiply these values:
[tex]\[ \text{Arc Length} ≈ 20.94 \text{ inches} \][/tex]
So, the approximate length of the arc is 20.94 inches, which corresponds to the option "20.94 inches".
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