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 arc length of a circle, you can use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Let's break down the problem:
1. Identify the radius and central angle:
- The radius of the circle is given as 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the formula for arc length:
Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the result:
First, multiply the radius by the central angle:
[tex]\[ = 10 \times \frac{2\pi}{3} \][/tex]
Simplifying this calculation gives you:
[tex]\[ \approx 20.94 \text{ inches} \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct option is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Let's break down the problem:
1. Identify the radius and central angle:
- The radius of the circle is given as 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Use the formula for arc length:
Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the result:
First, multiply the radius by the central angle:
[tex]\[ = 10 \times \frac{2\pi}{3} \][/tex]
Simplifying this calculation gives you:
[tex]\[ \approx 20.94 \text{ inches} \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct option is 20.94 inches.
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