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 :
Sure! To find the approximate length of the arc intersected by a central angle in a circle, we can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
In this problem, we have:
- Radius = 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 and Angle: We have a circle with a radius of 10 inches, and the central angle given is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Arc Length Formula: Use the formula for the arc length:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the Arc Length: Multiply the radius by the central angle:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Simplify the Expression: Perform the multiplication:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
5. Approximate the Value: Using the approximate value of [tex]\(\pi\)[/tex] (around 3.1416), calculate the arc length:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.1416}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \text{ inches} \][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the correct option is:
20.94 inches
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle} \][/tex]
In this problem, we have:
- Radius = 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 and Angle: We have a circle with a radius of 10 inches, and the central angle given is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Arc Length Formula: Use the formula for the arc length:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate the Arc Length: Multiply the radius by the central angle:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Simplify the Expression: Perform the multiplication:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
5. Approximate the Value: Using the approximate value of [tex]\(\pi\)[/tex] (around 3.1416), calculate the arc length:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.1416}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.94 \text{ inches} \][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the correct option is:
20.94 inches
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