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Coarse grains in a sample of Rhyolite suggest that it formed by ……
A-rapid cooling of molten rock materials at the Earth’s surface.
B-slow cooling of molten rock materials at the Earth’s surface.
C-rapid cooling of molten rock materials below the Earth’s surface.
D-slow cooling of molten rock materials below the Earth’s surface.

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    $\begingroup$ To discriminate between at surface or below surface, you have to look at the rock name. To discriminate between rapid or slow cooling, you have to look at the grain size. What does it tell you in terms of crystallization kinematics? $\endgroup$ Feb 25 at 10:37
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(This homework question is probably long overdue, but here is an answer for the sake of site statistics and future readers.)

Magmatic rocks are further classified into extrusive rocks (emplaced at the surface) and plutonic rocks (emplaced in the crust). A magma of the same (silicic) composition can yield a granite if emplaced as a pluton, or a rhyolite if emplaced at the surface. So to answer the first part, you just have to look at the rock's name: if it's a rhyolite, then it was formed at the Earth's surface.

As for the grain size, there is this classic diagram (here from Vernon 2018):

enter image description here

The diagram shows that if you cool a magma quickly (high undercooling), you get a lot of nucleation (a nucleus is like a crystal embryo) but not much crystal growth, so you end up with lots of small crystals in the rock. On the contrary, if you cool a magma slowly (low undercooling) you get few nucleation but more crystal growth, so you end up with less crystals, but bigger ones. (And if you cool very fast you have neither and end up with a glass, i.e., obsidian.) So here the answer is B: if you have coarse grains, then the cooling was slow.

Note that the question is bit tricky because normally, as rhyolite is emplaced at the surface, it cools quickly hence have fine grains, while coarse grains is usually typical of granite, which cools slower in the crust...

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Rhyolite by definition doesn’t have coarse grains. A rock with the composition of rhyolite that is completely coarse grained is going to be a granite or microgranite of some sort.

If what you are referring to are phenocrysts in the rhyolite (i.e. a rhyolite with porphyritic texture) or even crystals in a rhyolite tuff, then that is an indication that those crystals formed in the magma chamber and were suspended in the melt prior to extrusion of the rhyolite.

So if this is a test or homework question, it’s at best poorly worded. The answer is that larger grains in igneous rocks generally cool more slowly, deeper in the lithosphere. It’s not so straightforward, though. Crystal size is also affected by how quickly a magma is cooled. But rhyolite by definition is an extrusive rock which is erupted at the surface, and cools quite quickly, relatively. As mentioned above, any phenocrysts in the rhyolite would themselves have formed more slowly in the magma chamber or conduit, within the earth, but the rhyolite itself, a fine-grained rock, is molten when extruded and cools quickly.

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