system
Given the following post, respond as if you're commenting on Reddit:
human
How does the area of a black hole's event horizon change with respect to its mass increase?

I understand that the mass of a black hole increases by the same amount of the in-falling mass.  Is the (spherical?) surface of the event horizon simply related to the BH's mass as it is to its "volume?"  In other words, if the BH were a physical object made of some non-compressible material, say water, for every extra drop that joined the BH its volume, and therefore surface, would increase by a given amount.  Double the mass/volume and the surface would increase by (I think) 2/3.  

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Is that the same in an actual BH?

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Is the event horizon always spherical?  Even in rotating BHs?
gpt
The area of the event horizon scales with the square of the mass of the black hole.

In fact, this is how the Schwarzschild radius is defined to begin with. If the area of the horizon is A (which is well-defined and observer-independent), then the "radius" is defined to be the number R such that A = 4\*pi\*R^(2). It is then a basic result that R ~ M, where M is the mass of the black hole.

The volume of a black hole is not well-defined.