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Answer :
To find the length of an arc when given the angle in radians and the radius of the circle, we use the formula
[tex]$$
s = r\theta,
$$[/tex]
where
- [tex]$s$[/tex] is the arc length,
- [tex]$r$[/tex] is the radius of the circle, and
- [tex]$\theta$[/tex] is the angle in radians.
Given that the radius is [tex]$10$[/tex] inches and the angle is [tex]$\frac{2\pi}{3}$[/tex] radians, we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, we can substitute [tex]$\pi \approx 3.1416$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the length of the arc is approximately [tex]$20.94$[/tex] inches, which matches the answer choice "20.94 inches."
[tex]$$
s = r\theta,
$$[/tex]
where
- [tex]$s$[/tex] is the arc length,
- [tex]$r$[/tex] is the radius of the circle, and
- [tex]$\theta$[/tex] is the angle in radians.
Given that the radius is [tex]$10$[/tex] inches and the angle is [tex]$\frac{2\pi}{3}$[/tex] radians, we substitute these values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3} = \frac{20\pi}{3}.
$$[/tex]
To find an approximate numerical value, we can substitute [tex]$\pi \approx 3.1416$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the length of the arc is approximately [tex]$20.94$[/tex] inches, which matches the answer choice "20.94 inches."
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Rewritten by : Jeany
