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 in the circle, you can use the formula for arc length, which is:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how you can solve the problem using this formula:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The central angle is given in radians as [tex]\(\frac{2\pi}{3}\)[/tex].
2. Apply the Arc Length Formula:
- Plug the given radius and central angle into the formula.
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- First, multiply the radius (10 inches) by the central angle in radians [tex]\(\frac{2\pi}{3}\)[/tex].
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \, \text{inches}
\][/tex]
The approximate length of the arc is [tex]\(20.94 \, \text{inches}\)[/tex].
Therefore, the correct choice from the options given is:
- 20.94 inches
This matches the option of 20.94 inches from the list provided.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how you can solve the problem using this formula:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The central angle is given in radians as [tex]\(\frac{2\pi}{3}\)[/tex].
2. Apply the Arc Length Formula:
- Plug the given radius and central angle into the formula.
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- First, multiply the radius (10 inches) by the central angle in radians [tex]\(\frac{2\pi}{3}\)[/tex].
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \, \text{inches}
\][/tex]
The approximate length of the arc is [tex]\(20.94 \, \text{inches}\)[/tex].
Therefore, the correct choice from the options given is:
- 20.94 inches
This matches the option of 20.94 inches from the list provided.
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
