Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc intercepted 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 the arc of a circle, we use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Given:
- Radius of the circle = 10 inches
- Central angle = [tex]\(\frac{2\pi}{3}\)[/tex] radians
Let's calculate the arc length step-by-step:
1. Identify the values given:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex] radians
2. Use the formula for arc length:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
3. Substitute the known values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Carry out the multiplication:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
5. Approximate this expression using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.14159}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx \frac{62.8318}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.943951 \][/tex]
So, the approximate length of the arc is about 20.94 inches.
Based on the provided choices, the correct answer is:
20.94 inches
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Given:
- Radius of the circle = 10 inches
- Central angle = [tex]\(\frac{2\pi}{3}\)[/tex] radians
Let's calculate the arc length step-by-step:
1. Identify the values given:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex] radians
2. Use the formula for arc length:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
3. Substitute the known values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
4. Carry out the multiplication:
[tex]\[ \text{Arc Length} = \frac{20\pi}{3} \][/tex]
5. Approximate this expression using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[ \text{Arc Length} \approx \frac{20 \times 3.14159}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx \frac{62.8318}{3} \][/tex]
[tex]\[ \text{Arc Length} \approx 20.943951 \][/tex]
So, the approximate length of the arc is about 20.94 inches.
Based on the provided choices, the correct answer is:
20.94 inches
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