Cook Islands is about 6,277 times smaller than Alaska.

Alaska is approximately 1,481,348 sq km, while Cook Islands is approximately 236 sq km, making Cook Islands 0.02% the size of Alaska. Meanwhile, the population of Alaska is ~710,231 people (702,103 fewer people live in Cook Islands).
Tip: This to-scale comparison of Alaska vs. Cook Islands uses the Mercator projection, which distorts the size of regions near the poles.