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. The arc length [tex]\( L \)[/tex] is given by:
[tex]\[
L = \text{radius} \times \text{central angle in radians}
\][/tex]
In this problem, we have:
- Radius of the circle: 10 inches
- Central angle: [tex]\(\frac{2\pi}{3}\)[/tex] radians
Now, let's calculate the arc length step-by-step:
1. Identify the radius: The radius of the circle is given as 10 inches.
2. Identify the central angle: The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Apply the formula for arc length: Substitute the radius and the central angle into the formula:
[tex]\[
L = 10 \times \frac{2\pi}{3}
\][/tex]
4. Multiply the values:
[tex]\[
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
5. Approximate [tex]\( \pi \)[/tex] as 3.14159 to calculate the arc length numerically:
[tex]\[
L \approx \frac{20 \times 3.14159}{3}
\][/tex]
6. Calculate the final arc length:
[tex]\[
L \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
\][/tex]
Hence, the approximate length of the arc is 20.94 inches. The closest answer choice to this length is 20.94 inches.
[tex]\[
L = \text{radius} \times \text{central angle in radians}
\][/tex]
In this problem, we have:
- Radius of the circle: 10 inches
- Central angle: [tex]\(\frac{2\pi}{3}\)[/tex] radians
Now, let's calculate the arc length step-by-step:
1. Identify the radius: The radius of the circle is given as 10 inches.
2. Identify the central angle: The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
3. Apply the formula for arc length: Substitute the radius and the central angle into the formula:
[tex]\[
L = 10 \times \frac{2\pi}{3}
\][/tex]
4. Multiply the values:
[tex]\[
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
5. Approximate [tex]\( \pi \)[/tex] as 3.14159 to calculate the arc length numerically:
[tex]\[
L \approx \frac{20 \times 3.14159}{3}
\][/tex]
6. Calculate the final arc length:
[tex]\[
L \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
\][/tex]
Hence, the approximate length of the arc is 20.94 inches. The closest answer choice to this length is 20.94 inches.
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Rewritten by : Jeany
