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 use the formula for arc length, which is:
[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle in radians} \][/tex]
In this problem, we're given:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length step-by-step:
1. Identify the radius and central angle:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex] radians
2. Use the arc length formula:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \, \text{radians} \][/tex]
3. Calculate the arc length:
When you multiply these numbers, the approximate arc length you find is:
[tex]\[ \approx 20.94 \, \text{inches} \][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle in radians} \][/tex]
In this problem, we're given:
- The radius of the circle is 10 inches.
- The central angle is [tex]\(\frac{2\pi}{3}\)[/tex] radians.
Now, let's calculate the arc length step-by-step:
1. Identify the radius and central angle:
- Radius ([tex]\(r\)[/tex]) = 10 inches
- Central angle ([tex]\(\theta\)[/tex]) = [tex]\(\frac{2\pi}{3}\)[/tex] radians
2. Use the arc length formula:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Arc Length} = 10 \, \text{inches} \times \frac{2\pi}{3} \, \text{radians} \][/tex]
3. Calculate the arc length:
When you multiply these numbers, the approximate arc length you find is:
[tex]\[ \approx 20.94 \, \text{inches} \][/tex]
So, the approximate length of the arc is 20.94 inches. Therefore, the answer is 20.94 inches.
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Rewritten by : Jeany
