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 intercepted by a central angle in a circle, we use the formula:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Given:
- Radius ([tex]\( r \)[/tex]) = 10 inches
- Central Angle ([tex]\( \theta \)[/tex]) = [tex]\( \frac{2\pi}{3} \)[/tex] radians
Let's calculate the arc length step by step:
1. Identify the values:
- Radius is [tex]\( 10 \)[/tex] inches.
- Central Angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
2. Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- First, compute [tex]\( 10 \times \frac{2}{3} \)[/tex]:
[tex]\[ 10 \times \frac{2}{3} = \frac{20}{3} \][/tex]
- Then multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[ \frac{20}{3} \times 3.14159 \approx 20.94 \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct answer is:
20.94 inches
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
Given:
- Radius ([tex]\( r \)[/tex]) = 10 inches
- Central Angle ([tex]\( \theta \)[/tex]) = [tex]\( \frac{2\pi}{3} \)[/tex] radians
Let's calculate the arc length step by step:
1. Identify the values:
- Radius is [tex]\( 10 \)[/tex] inches.
- Central Angle is [tex]\( \frac{2\pi}{3} \)[/tex] radians.
2. Plug the values into the formula:
[tex]\[ \text{Arc Length} = 10 \times \frac{2\pi}{3} \][/tex]
3. Calculate:
- First, compute [tex]\( 10 \times \frac{2}{3} \)[/tex]:
[tex]\[ 10 \times \frac{2}{3} = \frac{20}{3} \][/tex]
- Then multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[ \frac{20}{3} \times 3.14159 \approx 20.94 \][/tex]
Therefore, the approximate length of the arc is 20.94 inches.
The correct answer is:
20.94 inches
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
