When the Alexandria Sanitation Authority held public hearings several months ago on a proposed 250 percent rate increase, there was very little comment from the public. In fact, says sanitation director Samuel L. lShafer, no one even bothered to show up for the hearing.

But this month, Alexandrians began howling about the increase when they received noticeably higher sewer bills.

The new rate 84 cents per 1,000 gallons , or roughly $73 a year for an average household, is the first increase for residential customers since the city built its sewer treatment plant in 1965. (The old rate was 24 cents for each 1,000 gallons of water).

Notices of the increase were sent out with water-sewer bills several months ago, but Shafer said many residents apparently were still surprised when their quarterly water-sewer bills jumped this month. January bills are the first to include a full three months with the new sewer rate.

About 30 city residents a day have been calling the privately owned Virginia-American Water Co., which collects sewer charges for the sanitation authority. Shafer said his agency also has been getting calls, but many residents apparently think the water company is in charge of city sewers.

The rate hike is paying for part of a $100 million expansion and modernization of the city plant beside the Beltway and Rte. 1.

The plant was required by the U.S. Enviromental Protection Agency under strict 1972 antipollution laws, and the EPA is paying for 75 percent of the advanced treatment plant. City officials have said operation of the plant will require the santation department to double its staff of 50 and will require large increases of chemicals and electric power to operate. Shafer noted, however, that another rate increase is not expected for at least five years.

The enlarged plant, already partially in use, will remove 99 percent of the pollutants in city sewage when it is completed in two years. Its capacity will be 54 million gallons a day, sufficient to serve a regional population of more than 40,000, including Fairfax County neighborhood south and west of the city.

Even with the new rate, the charges are lower than every jurisdiction in the area except the District, where an average household pays about $48 a year.

By comparison, yearly sewer charges for an average household in Arlington are $81, in Fairfax County $113, in Falls Church $100 and in Fairfax City, $172.