Kyle has a bicycle whose central gear has a radius of 3 inches. The gear on the rear wheel, which is connected to the central gear

by a bicycle chain, has a radius of 1.5 inches.

Part A: What distance would the chain travel if the central gear was rotated 225°? Explain your answer.

11.78 inches

Step-by-step explanation:

The chain travel will equal the length of the 225° arc on the central gear. Arc length (s) is given by the formula ...

s = rθ

where θ is the central angle in radians. We know that 180° is π radians, so the chain travel is ...

s = (3 in) (225°) (π/180°) = 15π/4 in ≈ 11.78 in