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 determine the length of an arc intercepted by a central angle in a circle, we use the formula
[tex]$$
\text{Arc Length} = r \theta,
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
In this problem, we are given:
- The radius [tex]$r = 10$[/tex] inches,
- The central angle [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
Using the formula, we calculate the arc length as follows:
[tex]$$
\text{Arc Length} = 10 \times \frac{2\pi}{3}.
$$[/tex]
First, multiply the constants:
[tex]$$
10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, note that
[tex]$$
\frac{20\pi}{3} \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
So, the correct answer is
[tex]$$
20.94 \text{ inches}.
$$[/tex]
[tex]$$
\text{Arc Length} = r \theta,
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
In this problem, we are given:
- The radius [tex]$r = 10$[/tex] inches,
- The central angle [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
Using the formula, we calculate the arc length as follows:
[tex]$$
\text{Arc Length} = 10 \times \frac{2\pi}{3}.
$$[/tex]
First, multiply the constants:
[tex]$$
10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, note that
[tex]$$
\frac{20\pi}{3} \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
So, the correct answer is
[tex]$$
20.94 \text{ inches}.
$$[/tex]
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!
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Rewritten by : Jeany
