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 intersected by a central angle in a circle, you can use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
In this case, the circle has:
- A radius of 10 inches.
- A central angle of [tex]\(\frac{2 \pi}{3}\)[/tex] radians.
Now, let's apply the values to the formula:
1. Identify the radius and central angle:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central Angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2 \pi}{3}\)[/tex] radians
2. Plug these values into the formula for arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2 \pi}{3}
\][/tex]
3. Calculate the arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2 \pi}{3} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. The correct answer from the given options is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
In this case, the circle has:
- A radius of 10 inches.
- A central angle of [tex]\(\frac{2 \pi}{3}\)[/tex] radians.
Now, let's apply the values to the formula:
1. Identify the radius and central angle:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central Angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2 \pi}{3}\)[/tex] radians
2. Plug these values into the formula for arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2 \pi}{3}
\][/tex]
3. Calculate the arc length:
[tex]\[
\text{Arc Length} = 10 \times \frac{2 \pi}{3} \approx 20.94 \text{ inches}
\][/tex]
Therefore, the approximate length of the arc is 20.94 inches. The correct answer from the given options is 20.94 inches.
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