Thank you for visiting A circle has a radius of 10 inches Find the approximate length of the arc subtended by an angle of tex frac 2 pi 3. 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 with an angle of [tex]\(\frac{2\pi}{3}\)[/tex] radians in a circle with a radius of 10 inches, follow these steps:
1. Understand Arc Length Formula:
The formula to find the length of an arc (arc length) in a circle is given by:
[tex]\[
\text{Arc Length} = \text{Angle in Radians} \times \text{Radius}
\][/tex]
2. Identify the Given Values:
- The radius of the circle (r) is 10 inches.
- The angle of the arc, given in radians, is [tex]\(\frac{2\pi}{3}\)[/tex].
3. Plug in the Values:
Using the formula:
[tex]\[
\text{Arc Length} = \left(\frac{2\pi}{3}\right) \times 10
\][/tex]
4. Calculate the Arc Length:
- First, calculate [tex]\(\frac{2\pi}{3}\)[/tex] which is a proportional part of the circle's circumference.
- Then multiply by the radius (10 inches) to find the actual arc length.
5. Find the Result:
The calculated arc length is approximately 20.94 inches.
So, the approximate length of the arc is 20.94 inches.
1. Understand Arc Length Formula:
The formula to find the length of an arc (arc length) in a circle is given by:
[tex]\[
\text{Arc Length} = \text{Angle in Radians} \times \text{Radius}
\][/tex]
2. Identify the Given Values:
- The radius of the circle (r) is 10 inches.
- The angle of the arc, given in radians, is [tex]\(\frac{2\pi}{3}\)[/tex].
3. Plug in the Values:
Using the formula:
[tex]\[
\text{Arc Length} = \left(\frac{2\pi}{3}\right) \times 10
\][/tex]
4. Calculate the Arc Length:
- First, calculate [tex]\(\frac{2\pi}{3}\)[/tex] which is a proportional part of the circle's circumference.
- Then multiply by the radius (10 inches) to find the actual arc length.
5. Find the Result:
The calculated arc length is approximately 20.94 inches.
So, the approximate length of the arc is 20.94 inches.
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