Question

A chain fits tightly around two gears as shown. The distance between the centers of the gears is 32 inches. The radius of the larger gear is 19 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale.

Answer 1

Explanation:

We can start by using the fact that the chain fits tightly around both gears, which means that the length of the chain is equal to the sum of the circumferences of the two gears. Let r be the radius of the smaller gear. Then we have:

circumference of larger gear + circumference of smaller gear = length of chain

2π(19) + 2π(r) = 32π

Simplifying this equation, we get:

38π + 2π(r) = 32π

2π(r) = -6π

r = -3