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Answer :
To solve this problem, we need to find the length of the arc formed by a central angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians in a circle with a radius of 10 inches.
Here are the steps we follow:
1. Understand the Formula: The formula to find the arc length [tex]\( L \)[/tex] when you know the radius [tex]\( r \)[/tex] of the circle and the central angle [tex]\( \theta \)[/tex] in radians is:
[tex]\[
L = r \cdot \theta
\][/tex]
2. Identify the Values:
- The radius [tex]\( r = 10 \)[/tex] inches.
- The central angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians.
3. Substitute into the Formula:
Substituting the given values into the arc length formula:
[tex]\[
L = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate:
- First, multiply 10 by [tex]\(\frac{2\pi}{3}\)[/tex]:
[tex]\[
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
5. Approximate the Result:
- Using [tex]\(\pi \approx 3.14159\)[/tex], calculate [tex]\(\frac{20 \times 3.14159}{3}\)[/tex]:
[tex]\[
L \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
\][/tex]
The approximate length of the arc is 20.94 inches. Therefore, among the choices given, the correct answer is 20.94 inches.
Here are the steps we follow:
1. Understand the Formula: The formula to find the arc length [tex]\( L \)[/tex] when you know the radius [tex]\( r \)[/tex] of the circle and the central angle [tex]\( \theta \)[/tex] in radians is:
[tex]\[
L = r \cdot \theta
\][/tex]
2. Identify the Values:
- The radius [tex]\( r = 10 \)[/tex] inches.
- The central angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians.
3. Substitute into the Formula:
Substituting the given values into the arc length formula:
[tex]\[
L = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate:
- First, multiply 10 by [tex]\(\frac{2\pi}{3}\)[/tex]:
[tex]\[
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
5. Approximate the Result:
- Using [tex]\(\pi \approx 3.14159\)[/tex], calculate [tex]\(\frac{20 \times 3.14159}{3}\)[/tex]:
[tex]\[
L \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
\][/tex]
The approximate length of the arc is 20.94 inches. Therefore, among the choices given, the correct 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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Rewritten by : Jeany
