Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc intersected by the angle tex frac 2 pi 3 tex. 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 of a circle when you are given the radius and an angle in radians, you can use the formula for arc length:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Angle in Radians} \][/tex]
Here's how you can solve the problem step-by-step:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Arc Length Formula:
- Substitute the given values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate:
- Multiply the radius by the angle:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
The approximate length of the arc is 20.94 inches.
So, based on the choices given, the correct answer is 20.94 inches.
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Angle in Radians} \][/tex]
Here's how you can solve the problem step-by-step:
1. Identify the Given Values:
- The radius of the circle is 10 inches.
- The angle is given as [tex]\(\frac{2\pi}{3}\)[/tex] radians.
2. Apply the Arc Length Formula:
- Substitute the given values into the formula:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3}
\][/tex]
3. Calculate:
- Multiply the radius by the angle:
[tex]\[
\text{Arc Length} = 10 \times \frac{2\pi}{3} \approx 20.94 \text{ inches}
\][/tex]
The approximate length of the arc is 20.94 inches.
So, based on the choices given, the correct answer is 20.94 inches.
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Rewritten by : Jeany
