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Two arcs of concentric circles are intercepted by the same central angle. The resulting arc length of the arc of the smaller circle is 36 ft and radius is 30 ft. The radius of thr larger circle is 45 ft. Find tye length of the corresponding arc of the larger circle.

Respuesta :

bhuvna789456

The length of the corresponding arc of the larger circle = 54 ft.

Step-by-step explanation:

step 1 :

  • "Concentric circles" have same center but different radius.
  • So, the angle formed by the arcs of the two circles with same center will also be same.

step 2 :

Small circle :

  • Length of the arc = 36 ft
  • Radius of the circle = 30 ft

Arc length = (∅/360)2πr

where,

∅ = arc angle

π = 3.14

r = radius of circle

step 3 :

Arc length = (∅/360)2[tex]\times[/tex]3.14[tex]\times[/tex]30

⇒ 36 = (∅/360)[tex]\times[/tex]188.4

⇒ ∅ = 36[tex]\times[/tex]360 / 188.4

∅ = 68.79

step 4 :

Large circle :

  • Radius of large circle = 45 ft
  • The arc angle, ∅ = 68.79

Arc length = (∅/360)2πr

                 = (68.79/360) 2[tex]\times[/tex]3.14[tex]\times[/tex]45

Arc length = 54 ft

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