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Answer :
To find the length of the arc in a circle when the radius and the central angle are given, we can use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
In this particular problem:
1. The radius of the circle is given as 10 inches.
2. The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, using the formula:
[tex]\[ \text{Arc Length} = 10 \times \left(\frac{2\pi}{3}\right) \][/tex]
This simplifies to:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
Calculating the approximate value:
[tex]\[ \text{Arc Length} \approx 20.94 \, \text{inches} \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct choice from the given options is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
In this particular problem:
1. The radius of the circle is given as 10 inches.
2. The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, using the formula:
[tex]\[ \text{Arc Length} = 10 \times \left(\frac{2\pi}{3}\right) \][/tex]
This simplifies to:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
Calculating the approximate value:
[tex]\[ \text{Arc Length} \approx 20.94 \, \text{inches} \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct choice from the given options is 20.94 inches.
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