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 solve for the length of the arc, we can use the formula for the arc length of a circle:
[tex]$$
s = r \theta
$$[/tex]
where:
- [tex]$s$[/tex] is the arc length,
- [tex]$r$[/tex] is the radius, and
- [tex]$\theta$[/tex] is the central angle in radians.
Given:
- The radius [tex]$r = 10$[/tex] inches,
- The central angle [tex]$\theta = \frac{2\pi}{3}$[/tex] radians,
we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
$$[/tex]
Now, to find the approximate numerical value, we use [tex]$\pi \approx 3.14159$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.14159}{3} \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
$$[/tex]
Thus, the approximate length of the arc is [tex]$\boxed{20.94 \text{ inches}}$[/tex].
[tex]$$
s = r \theta
$$[/tex]
where:
- [tex]$s$[/tex] is the arc length,
- [tex]$r$[/tex] is the radius, and
- [tex]$\theta$[/tex] is the central angle in radians.
Given:
- The radius [tex]$r = 10$[/tex] inches,
- The central angle [tex]$\theta = \frac{2\pi}{3}$[/tex] radians,
we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}
$$[/tex]
Now, to find the approximate numerical value, we use [tex]$\pi \approx 3.14159$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.14159}{3} \approx \frac{62.8318}{3} \approx 20.94 \text{ inches}
$$[/tex]
Thus, the approximate length of the arc is [tex]$\boxed{20.94 \text{ inches}}$[/tex].
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Rewritten by : Jeany
