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Answer :
To find the approximate length of the arc intersected by a central angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians in a circle with a radius of 10 inches, you can use the following formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how you can calculate it step-by-step:
1. Identify the Radius and Central Angle:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the Arc Length Formula:
- Substitute the known values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the Arc Length:
- Perform the multiplication:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches} \][/tex]
So, the approximate arc length is 20.94 inches.
The correct answer from the options provided is:
- 20.94 inches
This rounds to the third option: 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how you can calculate it step-by-step:
1. Identify the Radius and Central Angle:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the Arc Length Formula:
- Substitute the known values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the Arc Length:
- Perform the multiplication:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches} \][/tex]
So, the approximate arc length is 20.94 inches.
The correct answer from the options provided is:
- 20.94 inches
This rounds to the third option: 20.94 inches.
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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