You increase the surface area
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increase the surface area of a solid means to increase the area of solid
no
It will increase it, as more of the outer surface of the solid is incontact with the liquid that it is dissolving in. :)
A a solid figure on a flat surface is a plane figure (I do believe)
There is no such thing as "surface area" of "solubility" since the latter refers to the maximum concentration in the solution of a solid (or liquid) in a liquid. "Surface area", as applied to such a phenomenon is meaningless. However, by *increasing* the surface area of, say, a salt, by grinding it, will increase its solubility. Maybe *that* is what the questioner meant.