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 are given a circle with a radius of [tex]$10$[/tex] inches and a central angle of [tex]$\frac{2\pi}{3}$[/tex] radians. The length of the arc intercepted by the central angle is given by the formula
[tex]$$
s = r \theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle in radians.
Substituting the given values:
[tex]$$
s = 10 \cdot \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, we can use the approximation [tex]$\pi \approx 3.1416$[/tex]. Therefore,
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the length of the arc is approximately [tex]$20.94$[/tex] inches.
[tex]$$
s = r \theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle in radians.
Substituting the given values:
[tex]$$
s = 10 \cdot \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, we can use the approximation [tex]$\pi \approx 3.1416$[/tex]. Therefore,
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the length of the arc is approximately [tex]$20.94$[/tex] inches.
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Rewritten by : Jeany
