Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc intersected by a central angle of tex frac 2 pi. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the length of the arc of a circle, you can use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle in Radians} \][/tex]
Here, we have:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length:
1. Substitute the Values Into the Formula:
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \][/tex]
2. Calculate the Result:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \, \text{inches} \][/tex]
So, the approximate length of the arc is 20.94 inches.
Therefore, from the given options, the correct answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle in Radians} \][/tex]
Here, we have:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length:
1. Substitute the Values Into the Formula:
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \][/tex]
2. Calculate the Result:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \, \text{inches} \][/tex]
So, the approximate length of the arc is 20.94 inches.
Therefore, from the given options, the correct answer is 20.94 inches.
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