Question

It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track? ...?

Answer 1

 Length of outer track = sum of length of 10 pieces = circumference of the outer circle 


if R is the Radius of outer circle then... 

Circumference of the outer track = 2pi*R 


Similarly the circumference of the inner track (with radius r) = 2pi*r 


length of each outer piece is 3.4 inch more than length of inner piece 

So total outer length is 10*3.4 =34 inches more than the inner length. 


=> Outer Circumference - Inner Circumference = 34 inches 

=> 2pi*R - 2pi*r = 34 

=> 2pi(R -r) = 34 

=> R-r = 34/2pi = 5.41 inches 

=> R-r = Width of the track = 5.41 inches