Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc intersected by an angle of tex frac 2 pi 3. 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 for a circle with a radius of 10 inches that is intercepted by an angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians, we can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Angle in Radians} \][/tex]
Here are the steps to find the arc length:
1. Identify the given values:
- Radius of the circle ([tex]\(r\)[/tex]) = 10 inches
- Angle in radians ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex]
2. Substitute the values into the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the arc length:
- First, multiply the radius by the angle:
[tex]\[
10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
4. Approximate the result using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
\frac{20\pi}{3} \approx \frac{20 \times 3.14159}{3} \approx 20.94
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. The correct answer is 20.94 inches, which matches the choice of 20.94 inches from the options given.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Angle in Radians} \][/tex]
Here are the steps to find the arc length:
1. Identify the given values:
- Radius of the circle ([tex]\(r\)[/tex]) = 10 inches
- Angle in radians ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex]
2. Substitute the values into the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate the arc length:
- First, multiply the radius by the angle:
[tex]\[
10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
4. Approximate the result using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
\frac{20\pi}{3} \approx \frac{20 \times 3.14159}{3} \approx 20.94
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. The correct answer is 20.94 inches, which matches the choice of 20.94 inches from the options given.
Thank you for reading the article A circle has a radius of 10 inches Find the approximate length of the arc intersected by an angle of tex frac 2 pi 3. 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
