Maryland highway officials last night asked Montgomery County's state legislators to seek funds for five major projects in the county next year, including the long-awaited Rte. I-370, which would connect Interstate 270 and the future Shady Grove Metrorail station.

The five projects plus highway renovation work would cost $16.5 million next year -- $4 million more than the current year's highway spending in Montgomery. The added funds would come from an expected $40 million increase in revenue statewide from the gasoline tax enacted by the legislature this year.

The 2.7-mile I-370, designed to provide relief in the traffic-choked I-270 corridor where a moratorium on new development has been threatened because roads are inadequate, would take six years to complete at a total cost of $134 million. Only $6.7 million would be sought to start the project next year.

The highway planners outlined the projects at a public hearing before the county's delegation to the General Assembly. The delegation is expected to acquiesce substantially to their proposals.

The major projects recommended in addition to I-370 were:

* A new interchange on I-270 at Falls Road. It would be designed to alleviate the heavy traffic backup at Montrose Road and Rte. 28 in Rockville and give commuters an alternate route from Rockville's central business district.

* Widening of the Capital Beltway to eight lanes for a three-mile stretch from I-270 to Georgia Avenue.

* Widening of Georgia Avenue from two to four lanes over 3.1 miles from Rte. 28 to Rte. 108 in the Olney area.

* Widening of Layhill Road from two to four lanes over 2.7 miles from Georgia Avenue to the Argyle Club Road in Glenmont.