If you e letting water cool, does the rate of cooling decrease when the surface area increases?
This question makes no sense to me either. There is no such thing as “speed of cooling”. Speed is rate of change in distance. No distance rate of change matters in this system. “Rate of cooling” means change in temperature per change in time. This is the quantity that matters. And I don’t know who told you that increasing the surface area decreases the rate of cooling, but they are wrong. If you keep mass the same and spread out the system such that the surface area increases, the same rate of cooling will occur. There is a difference between rate of heat transfer and rate of cooling. Maybe that is what this question was asking. If you, rather than keep mass the same, increase mass and surface area, mass proportional to the cube of a linear dimension and surface area proportional to the square of a dimension, then maybe we can salvage this situation. Increasing surface area increases the rate of heat transfer. BUT, if you increase mass much more than you increase surface area, the rate
