Burning is a chemical process - oxidation - that usually takes place where oxygen from the air reacts with the substance that is burning. The surface area determines how much oxygen is in contact with the substance.
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For example, the amount of nutrients a cell can absorb are proportional to its surface area.
All chemical reactions take place on surfaces = so very important
so it can get more sun
It is not always the case. If you are out in the cold with insufficient clothing, the important thing - to prevent hypothermia - is to MINIMISE the surface to volume ratio.
Fungi make their food via absorption, and a large surface area makes nutrient absorption extremely efficient.