Is fire extinguisher is needed for a small room?

Fire extinguishers are required according to local, state or federal fire codes, as may apply to the particular structure. Some "small rooms" may need their own extinguishers.

Under the NFPA 1 Fire Code, nearly all types of occupancies other than one- and two-family dwellings are required to have at least one portable fire extinguisher, even if there are fire alarms, fire sprinklers and "fire-proof" construction. NFPA 1 (2009): Table 13.6.2 Portable Fire Extinguishers Required (by occupancy use).

For example:

There must be no less than one fire extinguisher within 75 feet of any Class A Hazard and within 30 or 50 feet of any Class B hazard (depending upon size of extinguisher and type of hazard). NFPA 1 (2009): Table 13.6.8.2.1.1 Fire Extinguisher Size and Placement for Class A Hazards and Table 13.6.8.3.1.1. for Class B Hazards.