Respuesta :

nicolina
Formula for arc lenght:
[tex]l = \frac{ \alpha }{360} 2r\pi[/tex]
Insert given data:
[tex]l = \frac{30}{360} \times 2 \times 12cm \times \pi[/tex]
[tex]l = 2\pi = 6.28cm[/tex]

Answer:

Let s be the length of the arc subtending an angle [tex]\sf{\theta}^{c}[/tex] at the centre of a circle of radius r.

Then,

[tex] \\ \theta \: = \sf \: \frac{s}{r} \\ [/tex]

Here,

  • r = 12 cm.
  • ∅ = 30°

[tex] \\ \implies \sf \: \bigg(30 \times \frac{\pi}{180} \bigg) {}^{c} \\ \\ \\ \implies \sf \blue{ \bigg({ \frac{\pi}{6} } \bigg)^{c} } \\ [/tex]

Therefore,

[tex] \\ \theta = \sf \: \dfrac{s}{r} \\ \\ \\ \implies \sf \: \frac{\pi}{6} = \frac{s}{12} \\ \\ \\ \implies \sf \red{s = \frac{12\pi}{6} cm. } \\ [/tex]

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