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Answer :
We are given a circle with a radius of [tex]$10$[/tex] inches and a central angle of
[tex]$$\frac{2\pi}{3} \text{ radians}.$$[/tex]
The formula to find the arc length ([tex]$s$[/tex]) of a circle is:
[tex]$$
s = r\theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle (in radians).
Substitute the given values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3}.
$$[/tex]
Multiply to simplify:
[tex]$$
s = \frac{20\pi}{3}.
$$[/tex]
To approximate the arc length, we use the approximation [tex]$\pi \approx 3.1416$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the arc length is approximately:
[tex]$$20.94 \text{ inches}.$$[/tex]
[tex]$$\frac{2\pi}{3} \text{ radians}.$$[/tex]
The formula to find the arc length ([tex]$s$[/tex]) of a circle is:
[tex]$$
s = r\theta,
$$[/tex]
where [tex]$r$[/tex] is the radius and [tex]$\theta$[/tex] is the central angle (in radians).
Substitute the given values into the formula:
[tex]$$
s = 10 \times \frac{2\pi}{3}.
$$[/tex]
Multiply to simplify:
[tex]$$
s = \frac{20\pi}{3}.
$$[/tex]
To approximate the arc length, we use the approximation [tex]$\pi \approx 3.1416$[/tex]:
[tex]$$
s \approx \frac{20 \times 3.1416}{3} \approx \frac{62.832}{3} \approx 20.94 \text{ inches}.
$$[/tex]
Thus, the arc length is approximately:
[tex]$$20.94 \text{ inches}.$$[/tex]
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Rewritten by : Jeany
