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 approximate length of the arc of a circle with a given radius and central angle, you can use the formula for arc length:
[tex]\[ L = r \times \theta \][/tex]
where:
- [tex]\( L \)[/tex] is the arc length,
- [tex]\( r \)[/tex] is the radius of the circle, and
- [tex]\( \theta \)[/tex] is the central angle in radians.
In this problem, the radius [tex]\( r \)[/tex] is 10 inches, and the central angle [tex]\( \theta \)[/tex] is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Let's plug these values into the formula:
1. Use the radius [tex]\( r = 10 \)[/tex] inches.
2. Use the angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians.
Substitute these values into the formula:
[tex]\[ L = 10 \times \frac{2\pi}{3} \][/tex]
Calculating the arc length:
[tex]\[ L = \frac{20\pi}{3} \][/tex]
When calculated, this value is approximately:
[tex]\[ L \approx 20.94 \][/tex] inches
Therefore, the approximate length of the arc is 20.94 inches. The closest answer choice to this calculation is 20.94 inches, which matches the option 20.94 inches.
[tex]\[ L = r \times \theta \][/tex]
where:
- [tex]\( L \)[/tex] is the arc length,
- [tex]\( r \)[/tex] is the radius of the circle, and
- [tex]\( \theta \)[/tex] is the central angle in radians.
In this problem, the radius [tex]\( r \)[/tex] is 10 inches, and the central angle [tex]\( \theta \)[/tex] is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Let's plug these values into the formula:
1. Use the radius [tex]\( r = 10 \)[/tex] inches.
2. Use the angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians.
Substitute these values into the formula:
[tex]\[ L = 10 \times \frac{2\pi}{3} \][/tex]
Calculating the arc length:
[tex]\[ L = \frac{20\pi}{3} \][/tex]
When calculated, this value is approximately:
[tex]\[ L \approx 20.94 \][/tex] inches
Therefore, the approximate length of the arc is 20.94 inches. The closest answer choice to this calculation is 20.94 inches, which matches the 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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Rewritten by : Jeany
