The question asks about the texture characteristic of rapidly cooled volcanic rocks. Let's analyze the options one by one:
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Pegmatitic: This texture is typically found in plutonic rocks and is characterized by exceptionally large crystal sizes, usually formed from very slowly cooled magmas deep underground. It is not associated with rapidly cooled volcanic rocks.
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Phaneritic: This texture is found in intrusive igneous rocks, where crystals are large enough to be seen with the naked eye, indicating slow cooling below the Earth's surface. Like pegmatitic, it is not indicative of rapid cooling.
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Porphyritic: This texture consists of large crystals (phenocrysts) embedded in a finer-grained groundmass. It implies two stages of cooling: slow cooling for the phenocrysts, followed by faster cooling for the groundmass. While it includes rapid cooling, it is not characteristic of it exclusively.
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Aphanitic: This texture is defined by very small crystals that are typically too small to be seen unaided. It forms when lava cools rapidly at or near the Earth's surface, preventing large crystals from growing. This is distinctly characteristic of rapidly cooled volcanic rocks.
Based on the analysis, apahnitic texture is indeed the one that forms when molten rock cools quickly, such as in volcanic environments. Hence, the correct answer is Aphanitic.
This texture occurs in extrusive igneous rocks, such as basalt, which are formed on the surface of the Earth where the cooling of molten lava happens rapidly.