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 an arc intercepted by a central angle in a circle, we use the formula:
[tex]$$
\text{Arc Length} = r \times \theta
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
In this problem, the radius is given as [tex]$r = 10$[/tex] inches and the central angle is [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
Substitute the given values into the formula:
[tex]$$
\text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
$$[/tex]
To find the approximate numerical value, we use the approximation [tex]$\pi \approx 3.14$[/tex]:
[tex]$$
\text{Arc Length} \approx \frac{20 \times 3.14}{3} \approx \frac{62.8}{3} \approx 20.93 \text{ inches}
$$[/tex]
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
[tex]$$
\text{Arc Length} = r \times \theta
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
In this problem, the radius is given as [tex]$r = 10$[/tex] inches and the central angle is [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
Substitute the given values into the formula:
[tex]$$
\text{Arc Length} = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
$$[/tex]
To find the approximate numerical value, we use the approximation [tex]$\pi \approx 3.14$[/tex]:
[tex]$$
\text{Arc Length} \approx \frac{20 \times 3.14}{3} \approx \frac{62.8}{3} \approx 20.93 \text{ inches}
$$[/tex]
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
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Rewritten by : Jeany
