In what way is surface area more important for cells than volume?

As a cell grows in size, the surface area gets bigger, but the volume gets bigger faster. Thinking about this as a ratio (division), the volume is the denominator and the surface area is the numerator. If the volume is getting very big, then the ratio itself will be getting very small.

the transfer for conduction is the heat transfering from the liquid to the spoon

the transfer for convection is the heat rising from the liquid to the air

the transfer for radiation is the heat going through the sides of the cup and to the air

at least that is what i would do