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 an arc in a circle, we need two pieces of information: the radius of the circle and the measure of the central angle that intercepts the arc, given in radians.
Here’s how you can find the arc length step by step:
1. Identify the given values:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the formula for arc length:
[tex]\[
\text{Arc length} = \text{Radius} \times \text{Central Angle (in radians)}
\][/tex]
3. Plug the values into the formula:
[tex]\[
\text{Arc length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate the product:
- First, multiply 10 by [tex]\(\frac{2\pi}{3}\)[/tex].
- This results in the approximate arc length of about 20.94 inches.
Therefore, the approximate length of the arc is 20.94 inches. Among the choices provided, the answer is 20.94 inches.
Here’s how you can find the arc length step by step:
1. Identify the given values:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the formula for arc length:
[tex]\[
\text{Arc length} = \text{Radius} \times \text{Central Angle (in radians)}
\][/tex]
3. Plug the values into the formula:
[tex]\[
\text{Arc length} = 10 \times \frac{2\pi}{3}
\][/tex]
4. Calculate the product:
- First, multiply 10 by [tex]\(\frac{2\pi}{3}\)[/tex].
- This results in the approximate arc length of about 20.94 inches.
Therefore, the approximate length of the arc is 20.94 inches. Among the choices provided, the answer is 20.94 inches.
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Rewritten by : Jeany
