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:
[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle (in radians)} \][/tex]
Here's how you can solve the problem step-by-step:
1. Identify the given values:
- Radius ([tex]\( r \)[/tex]) of the circle is 10 inches.
- Central angle ([tex]\( \theta \)[/tex]) is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate:
- First, calculate the product inside the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
4. Convert [tex]\(\frac{20\pi}{3}\)[/tex] to a numerical value:
- Using [tex]\(\pi \approx 3.14159\)[/tex], the calculation would be:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3} \approx 20.94 \text{ inches}
\][/tex]
5. Conclusion:
The approximate length of the arc is 20.94 inches.
Therefore, the correct answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle (in radians)} \][/tex]
Here's how you can solve the problem step-by-step:
1. Identify the given values:
- Radius ([tex]\( r \)[/tex]) of the circle is 10 inches.
- Central angle ([tex]\( \theta \)[/tex]) is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the arc length formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate:
- First, calculate the product inside the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
\][/tex]
4. Convert [tex]\(\frac{20\pi}{3}\)[/tex] to a numerical value:
- Using [tex]\(\pi \approx 3.14159\)[/tex], the calculation would be:
[tex]\[
\text{Arc Length} \approx \frac{20 \times 3.14159}{3} \approx 20.94 \text{ inches}
\][/tex]
5. Conclusion:
The approximate length of the arc is 20.94 inches.
Therefore, the correct answer is 20.94 inches.
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