Cocos (Keeling) Islands is about 7,575 times smaller than Ohio.

Ohio is approximately 106,056 sq km, while Cocos (Keeling) Islands is approximately 14 sq km, making Cocos (Keeling) Islands 0.01% the size of Ohio. Meanwhile, the population of Ohio is ~11.5 million people (11.5 million fewer people live in Cocos (Keeling) Islands).
Tip: This to-scale comparison of Ohio vs. Cocos (Keeling) Islands uses the Mercator projection, which distorts the size of regions near the poles.