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 intersected by a central angle, you can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how we can use this formula step-by-step:
1. Identify the given values:
- Radius of the circle is 10 inches.
- Central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
4. Approximate using π ≈ 3.14159:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.14159}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx \frac{62.8318}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \][/tex]
Therefore, the approximate length of the arc is 20.94 inches. From the given options, the closest answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how we can use this formula step-by-step:
1. Identify the given values:
- Radius of the circle is 10 inches.
- Central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
4. Approximate using π ≈ 3.14159:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.14159}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx \frac{62.8318}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \][/tex]
Therefore, the approximate length of the arc is 20.94 inches. From the given options, the closest answer is 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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