Question

26. Critique Reasoning Two gears on a bicycle have the shape of circles.

Gear 1 has a diameter of 4 inches, and gear 2 has a diameter of 2 inches.
Justin says that the circumference of gear 1 is 2 inches more than the
circumference of gear 2. Do you agree? Explain your answer using
proportional reasoning.​

Answer 1

Answer: I don't agree

The circumference of a circle is proportional to its diameter, the proportionality constant being π:

C = πd

π is a little more than 3.

The gears' diameters differ by 2 inches. The circumferences (and their difference) will scale proportionally so will differ by 2π inches, which is more than 6 inches.