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Carlos builds a robot that moves on small wheels. Each wheel has six 5-inch-long metal spokes that meet in the center. What the length of an arc between two consecutive spokes?

Express your answer as a simplified fraction in terms of \piπ.

Carlos builds a robot that moves on small wheels Each wheel has six 5inchlong metal spokes that meet in the center What the length of an arc between two consecu class=

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oladayoademosu

The length of an arc between two consecutive spokes is 5π/8 in.

Length of an arc

The length of an arc L = rФ where

  • r = radius of circle = 5 in/2 = 2.5 in and
  • Ф = angle subtended by arc in radians = 2π/n where
  • n = number of sectors in circle = 8

So, L = rФ

L = r × 2π/n

L = 2πr/n

Substituting the values of the variables into the equation, we have

L = 2πr/n

L = 2π × 2.5 in/8

L = 5π/8 in

So, the length of an arc between two consecutive spokes is 5π/8 in.

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