Bug Jar Race

Problem Statement
Jamal and Terry have circular bug jars of different dimensions. The boys each capture one bug and watch them run around the circular base of the bug jars. Jamal challenges Terry to a bug race, but he needs to determine a distance for the race in each of the respective jars that would be fair to both bugs.

Jamal’s bug jar has a diameter of 18 cm. Terry’s bug jar has a diameter of 12 cm. Jamal decides that it would be best if the bugs run one complete turn in Terry’s smaller jar.

a) How many centimeters long is the race?

b) What is the arc measure of the racetrack in Jamal’s bug jar?

Bug Jar.png
Note, these are not drawn to scale.

Credit: Glass Canister/Jar by CMA

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June 2014 - Okay