Is it possible that I overlooked something simple or is there a very complex answer to this? I looked online for an answer to this but couldn't find anything. I asked my teacher why this is, and he said that he didn't know and that it would be an interesting topic to further research. Then I ran into a question about the rate of change of a cube's volume I simply assumed that the rate of change would be the the surface area again because that seemed pretty sensible, turns out that it isn't, when you take the derivative of the volume of a cube (s^3), you get 3s^2 (using exponent rule) that isn't equal to the surface area of a cube, which is 6s^2. I'm using a calculus book and it asked a few questions about rate of change one of them being what is the rate of change of a sphere's volume, when I found the rate of change it turned out to be the surface area of the sphere, this seemed pretty sensible because when you increase the volume of a sphere by a little bit you are increasing it by the current surface area. I have a question about the rate of change of spheres versus cubes so here goes:
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