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 intersected by a central angle in a circle, we can use the formula for arc length:
[tex]\[
\text{Arc Length} = \text{radius} \times \text{central angle (in radians)}
\][/tex]
Here, we have:
- A circle with a radius ([tex]\(r\)[/tex]) of 10 inches.
- A central angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Plug these values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
Carrying out the multiplication:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
To find the approximate numerical value, we can use the approximation [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3}
\][/tex]
Calculating:
[tex]\[
\text{Arc Length} \approx \frac{62.8318}{3} \approx 20.94
\][/tex]
Thus, the approximate length of the arc is 20.94 inches.
Therefore, the correct answer is approximately 20.94 inches, which matches option 20.94 inches in the given choices.
[tex]\[
\text{Arc Length} = \text{radius} \times \text{central angle (in radians)}
\][/tex]
Here, we have:
- A circle with a radius ([tex]\(r\)[/tex]) of 10 inches.
- A central angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Plug these values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
Carrying out the multiplication:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3}
\][/tex]
To find the approximate numerical value, we can use the approximation [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3}
\][/tex]
Calculating:
[tex]\[
\text{Arc Length} \approx \frac{62.8318}{3} \approx 20.94
\][/tex]
Thus, the approximate length of the arc is 20.94 inches.
Therefore, the correct answer is approximately 20.94 inches, which matches option 20.94 inches in the given choices.
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Rewritten by : Jeany
