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the larger the surface area you have, to more heat that you are going to lose.
Heat loss of water: The surface area effects the the rate of heat loss because the rate of heat loss increases if the surface are is higher. How: The water is spread out into a bigger space meaning the
Increasing the Surface Area increases the heat loss. You will find a nice example in the related question link below.
Surface area is a factor in the efficiency of heat exchange. A greater surface to mass ratio creates a faster transfer of heat. This is why the heat sink on your CPU has the multiple bars that increase its surface area. If it was just a solid cube (or worse yet a sphere), it would not have nearly the potential to remove heat from the CPU. Other factors in heat loss or dissipation include temperature differential, humidity, air circulation, and the chemical composition of the materials used.
You use surface area whenever you want to know the area of a non-flat surface. This is useful in a lot of physical applications. For example, heat flow, electrical current flow, or fluid flow through an irregularly-shaped region all are defined in terms of integrals over the boundary, and integration is taken with respect to surface area.