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The characteristics that many island countries in the Pacific Ocean share is that they experience significant seismic activity. This is because of the Pacific Rim and the plates are under these islands.
The name for such a hole is "caldera" which is a word of Spanish origin meaning "a pot" or a "cooking pot" (thing of cauldron!) - and this word is used because it resembles the shape of this hole.
Often the Calderas are filled with water forming lakes and often there is an island in the middle of the water.