How large a surface area in units of square feet will 1 gallon of paint cover if you apply a coat of paint that is 0.1 centimeter thick?

A gallon of paint covers about 300 square feet at a usual thickness of one coat; your example of 0.1 cm thick is very thick coat, equivalent to about 6 coats of paint at least; you could cover about 300/6 =50 square feet at that thickness.