The Rockville City Council this week voted unanimously to pay for a study of a 38-acre lake and park project being considered for a site 2,000 feet north of Montrose Road and east of Rte. I-270.

About half the cost of the $4 million project would come from funds the city collects from developers for its storm water management program. Under state and city law, developers must land is graded and cleared for housing tracts. Instead of building their own retention ponds, most developers have opted to make contribution to the city's program.

The city, according to public works director Gerald E. Morningstar, then may choose an appropriate spot along the stream valley altered by new development to build a holding pool. Morningstar told the council the city now has $831,833 in its storm water management fund, and estimated the amount will top $4 million by fiscal year 1987.

The council chose Greenhorne & O'mara, a Greenbelt consulting firm, to study the site and propose a design for the lake project. The firm will be paid $45,500.

The design work, Morningstar said after the Monday meeting, will take about 15 months. The lake is to fill 14 acres, and would cover 24 acres after heavy storms, Morningstar added.

Funds for the park facilities, to include boating, bike trails, picnic and playground areas and an amphitheater, have not yet been lined up, but Morningstar said the city probably will seek state assistance. He estimated the lake could be completed within three years, and the park could be finished two years later.

In other business, the council voted unanimously to move ahead with a plan to permit homeowners to divide their houses into two apartments, an attempt to ease the shortage of rental housing and allow homeowners to make extra income.

Edward J. Duffy, the city's community development specialist, told the council it would cost about $11,000 to convert a single-family house into two apartments.