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If two concentric circles have radii of 4 cm and 5 cm, how much longer, in cm, is the intercepted arc in the larger circle than an intercepted arc in the smaller circle for a central angle that is π2 radians?

Respuesta :

Answer:

[tex]\dfrac{\pi}{2} cm[/tex]

Step-by-step explanation:

Given two concentric circles where:

  • Radius of the Larger Circle =5
  • Radius of the smaller circle=4

Length of the intercepted arc for a central angle of [tex]\dfrac{\pi}{2} =\dfrac{\frac{\pi}{2} }{2\pi} X2\pi r=\dfrac{\pi r}{2}[/tex]

For the larger circle of radius 5cm, Length of the intercepted arc[tex]=\dfrac{5\pi}{2}[/tex]

For the smaller circle of radius 4cm, Length of the intercepted arc[tex]=\dfrac{4\pi}{2}[/tex]

Difference in Arc length

[tex]=\dfrac{5\pi}{2}-\dfrac{4\pi}{2}\\=\dfrac{\pi}{2} cm[/tex]

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