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 the arc, we use the formula
[tex]$$
s = r \theta,
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
Given that the radius is [tex]$10$[/tex] inches and the central angle is [tex]$\frac{2\pi}{3}$[/tex] radians, we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3}.
$$[/tex]
Next, we compute the product:
[tex]$$
s \approx 10 \times 2.0943951023931953 \approx 20.94395102393195.
$$[/tex]
Thus, the approximate arc length is [tex]$20.94$[/tex] inches.
This matches the answer choice:
[tex]$$\textbf{20.94 inches}.$$[/tex]
[tex]$$
s = r \theta,
$$[/tex]
where:
- [tex]$r$[/tex] is the radius of the circle,
- [tex]$\theta$[/tex] is the central angle in radians.
Given that the radius is [tex]$10$[/tex] inches and the central angle is [tex]$\frac{2\pi}{3}$[/tex] radians, we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3}.
$$[/tex]
Next, we compute the product:
[tex]$$
s \approx 10 \times 2.0943951023931953 \approx 20.94395102393195.
$$[/tex]
Thus, the approximate arc length is [tex]$20.94$[/tex] inches.
This matches the answer choice:
[tex]$$\textbf{20.94 inches}.$$[/tex]
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Rewritten by : Jeany
