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THis came up in a PbP we´re playing on the boards here.
A Ninja threw a Smoke Bomb, which has a radius of 15´ but acts like a Smoke Stick, which acts like Fog Cloud.
The question came up whether or not this was a Sphere effect or a Cylinder. (it mattered in the game because it affected whether a Large size creature on the edge of the AoE had Line of Sight to a Caster in order to ID their spell)
Some opinions wanted to defer to the source spells to further specify the shape of the AoE, essentially transposing the 15´ radius from the Smoke Bomb text itself onto the 20´ radius + 20´ height given by Fog Cloud, and assuming this was a cylinder. My take was that the AoE was solely defined by Smoke Bomb itself, and only the smoke´s effects were defined by Fog Cloud.
In any case, the question is, if an effect gives as it´s AoE:
* 15´radius (alone), is that a sphere or a cylinder?
* 20´radius + 20´height (as Fog Cloud), is that a sphere or a cylinder?
From a search of the PRD:
I found NO spells which contained the word ´cylinder´ which didn´t have that in their Target line - ALL had the format ´cylinder (x radius, x high)´ (as in Flame Strike, Sleet Storm). Spells containing the word ´sphere´ (like Invis Sphere or Prism. Sphere) used EITHER ´X radius sphere´ OR simply ´X radius (emanation)´ WITHOUT mentioning sphere in the Target line... Since we KNOW those are spherical spells (as they explicitly use that term in their name, even if not in the Area line), it´s clear that ´sphere´ isn´t being consistently described in spell stat-blocks... This could be fixed via Errata. But going from what we have, to me ´X radius´ (alone) would seem to ´default´ to a sphere - which is geometrically correct of course.
Fog Cloud ITSELF is especially questionable, since it´s giving both radius and height, which is superfluous for a spherical AoE, yet either a sphere or cylinder would seem equally plausible IMHO. (i.e. either it has an superfluous height listed when not needed, or doesn´t mention that it´s a Cylinder Area like EVERY other spell that contains the word Cylinder)
Also, the description for Cylinder area says ´you select the spell's point of origin. This point is the center of a horizontal circle, and the spell shoots down from the circle´ which makes sense for Flame Strike and Sleet Storm, but not so much for a Smoke Bomb. In fact, the ´down from (the center)´ read literally would mean nobody would be affected if it triggered at ground level.
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The height measurement for fog cloud is superfluous; if you cast it while floating in air, it would spread 20' in all directions, including height. In other words: "20-ft. radius" and "20-ft. radius, 20 ft. high" are the same thing, one just takes longer to read.
Unless an area of effect is specified as a cylinder (or something else), assume it is a radius (which, to answer your question, means sphere, but the game avoids using that term to avoid confusion, as the shape represented on the grid by a radius effect is not a sphere).
Unless told otherwise by some source in the spell/effect description I always assume that an effect given as an "x ft. radius" is spherical (or at least the weird grid approximation of a sphere that pathfinder uses).