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 for arc length:
[tex]\[
\text{Arc Length} = \text{Radius} \times \text{Central Angle in Radians}
\][/tex]
Here, the radius of the circle is given as 10 inches, and the central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, we can calculate the arc length:
1. Identify the Radius and Central Angle
- Radius [tex]\( r = 10 \)[/tex] inches
- Central Angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians
2. Substitute these values into the formula
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Perform the multiplication
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
The approximate arc length of the circle is [tex]\(20.94\)[/tex] inches. Therefore, among the given options, the correct length of the arc is:
20.94 inches.
[tex]\[
\text{Arc Length} = \text{Radius} \times \text{Central Angle in Radians}
\][/tex]
Here, the radius of the circle is given as 10 inches, and the central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, we can calculate the arc length:
1. Identify the Radius and Central Angle
- Radius [tex]\( r = 10 \)[/tex] inches
- Central Angle [tex]\( \theta = \frac{2\pi}{3} \)[/tex] radians
2. Substitute these values into the formula
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Perform the multiplication
[tex]\[
\text{Arc Length} \approx 20.94 \text{ inches}
\][/tex]
The approximate arc length of the circle is [tex]\(20.94\)[/tex] inches. Therefore, among the given options, the correct length of the arc is:
20.94 inches.
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