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 :
We start with the formula for the length of an arc:
[tex]$$
L = r \theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle in radians.
1. The given radius is [tex]$r = 10$[/tex] inches.
2. The given central angle is [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
3. Substitute the values into the formula:
[tex]$$
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
4. Evaluating [tex]$\frac{20\pi}{3}$[/tex] numerically gives approximately [tex]$20.94$[/tex] inches.
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
[tex]$$
L = r \theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle in radians.
1. The given radius is [tex]$r = 10$[/tex] inches.
2. The given central angle is [tex]$\theta = \frac{2\pi}{3}$[/tex] radians.
3. Substitute the values into the formula:
[tex]$$
L = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
4. Evaluating [tex]$\frac{20\pi}{3}$[/tex] numerically gives approximately [tex]$20.94$[/tex] inches.
Thus, the approximate length of the arc is [tex]$20.94$[/tex] inches.
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Rewritten by : Jeany
