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