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, we use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how we solve the problem step-by-step:
1. Identify the Radius and Central Angle:
- The radius of the circle is given as 10 inches.
- The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Formula:
- Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- Multiply the radius by the central angle:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Simplify:
- When you calculate this product, it gives approximately 20.94 inches.
Therefore, the approximate length of the arc is 20.94 inches, which matches the choice of 20.94 inches provided in the given options.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
Here's how we solve the problem step-by-step:
1. Identify the Radius and Central Angle:
- The radius of the circle is given as 10 inches.
- The central angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Formula:
- Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- Multiply the radius by the central angle:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Simplify:
- When you calculate this product, it gives approximately 20.94 inches.
Therefore, the approximate length of the arc is 20.94 inches, which matches the choice of 20.94 inches provided in the given options.
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Rewritten by : Jeany
