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Class-A fires

The most common method to control a class-A fire is to remove heat by spraying the burning solid fuels with water. Another method of controlling a class-A fire would be to reduce the oxygen content of the atmosphere in the immediate vicinity of the (i.e., "smother" the fire), such as by the introduction of an inert gas such as carbon dioxide.
In a Wildfire, fire control includes various wildland fire suppression techniques such as defensible space, opening the fuel ladder spacing, removing fuel in the fire's path with firebreaks and backfires, to minimize the brushfire from reaching new combustible fuel and spreading further.

Class-B fires

Some Class-B fires (hydrocarbons, petroleums, and fuels on fire) cannot be efficiently controlled with water. Fuels with a specific gravity less than water, such as gasoline or oil, float on water, resulting in the fire continuing in the fuel on top of the water. The application of a combination of fire suppressant foam mixed with water is a common and effective method of forming a blanket on top of the liquid fuel which eliminates the oxygen needed for combustion.The configuration of some fuels, such as coal and baled waste paper, result in a deep seated and burrowing fire, resulting in less effective fire control by the application of water on the outer surfaces of the fuel.
Some class-B fires can be controlled with the application of chemical fire suppressants.

Class-C

fires involve electricity as a continuous power source for the ignition of the fuels associated with electrical equipment, such as plastic cable jackets. The application of water does not always result in effective fire control, and there is a general concern regarding conductivity and personnel safety. Class C fires can be effectively controlled by removing the oxygen. The removal of electricity as a continuous ignition source is important to eliminate re-ignition. Once the electricity is removed, the result is a Class A fire.

Ventilation

Fires can spread through the interior of a structure as the hot gases spread due to the expansion of the gases as a result of the combustion. Some fires can be partially controlled by venting these gases to the outside through manufactured heat vents in the structure's roof, or by the fire department cutting holes in the roof.

From wiki.