Cocos (Keeling) Islands is about 12,744 times smaller than Missouri.

Missouri is approximately 178,414 sq km, while Cocos (Keeling) Islands is approximately 14 sq km, making Cocos (Keeling) Islands 0.01% the size of Missouri. Meanwhile, the population of Missouri is ~6.0 million people (6.0 million fewer people live in Cocos (Keeling) Islands).
Tip: This to-scale comparison of Missouri vs. Cocos (Keeling) Islands uses the Mercator projection, which distorts the size of regions near the poles.