kailuhanexo56
contestada

PLEASE HELP!
Both circle A and circle B have a central angle measuring 140°. The ratio of the radius of circle A to the radius of circle B is
2/3. If the length of the intercepted arc for circle A is
3/4π, what is the length of the intercepted arc for circle B?

Respuesta :

carlosego
The arc length is:
 S = R * theta
 Where,
 R: Radio
 Theta: central angle
 Substituting values we have:
 Circle A:
 Sa = Ra * (140/360) * 2π
 Circle B:
 Sb = Rb * (140/360) * 2π
 The relationship of arcs is:
 Sa / Sb = (Ra * (140/360) * 2π) / (Rb * (140/360) * 2π)
 Rewriting:
 Sa / Sb = (Ra / Rb)
 Substituting values:
 (3 / 4π) / Sb = 2/3
 Clearing Sb
 Sb = (3/2) (3 / 4π)
 Sb = (9 / 8π)
 Answer:
 The length of the intercepted arc for circle B is:
 Sb = (9 / 8π)

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