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 an arc in a circle, when you know the radius and the central angle in radians, you can use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Given that the radius of the circle is 10 inches and the central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians, you can plug these values into the formula:
1. Identify given values:
- Radius [tex]\( r = 10 \)[/tex] inches
- Central angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians
2. Use the arc length formula:
[tex]\[
\text{Arc Length} = r \times \theta
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
Thus, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Given that the radius of the circle is 10 inches and the central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians, you can plug these values into the formula:
1. Identify given values:
- Radius [tex]\( r = 10 \)[/tex] inches
- Central angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians
2. Use the arc length formula:
[tex]\[
\text{Arc Length} = r \times \theta
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate:
[tex]\[
\text{Arc Length} = \frac{20\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
Thus, the approximate length of the arc is 20.94 inches. Therefore, the correct answer is 20.94 inches.
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