Sri Lanka's hopes rest on the shoulders of Kumar Sangakkara

Kumar Sangakkara hit an unbeaten century as Sri Lanka reached 247-3 chasing a record 507 for victory in the second Test against Australia.

The hosts declared at 210-2 late on the morning of the fourth day in Hobart.

Sri Lanka rapidly lost their first wicket, Mitchell Johnson removing Michael Vandrort for four.

But Marvan Atapattu (80) and Sangakkara (109no) put on 143 for the second wicket, before Mahela Jayawardene fell first ball to a fired up Brett Lee.

"You've got to be realistic that 507 is a massive ask but the direction in which we go to tomorrow is now basically up to us," said Sangakkara.

"If we can get through to lunch without losing a wicket and depending on the amount of runs we get then things get a lot clearer.

"I don't really want to be a soothsayer and say what will happen, but we always go into the middle with a lot of belief and we try as best."

606: DEBATE For those who think that sustained Aussie dominance is a bad thing for the game, I suggest that you either get used to it, or find another sport to follow. FTS

Australia ensured Muttiah Muralitharan would have to wait until the home series against England to have the chance to overhaul Australia leg-spinner Shane Warne as the leading wicket-taker in Test history.

The Sri Lanka off-spinner took 1-90 in the second innings and will leave Australia still five wickets short of breaking Warne's record of 708 wickets.

During the series the 35-year-old spinner took four wickets for 400 runs, a sharp contrast to his career average of 21.77.

Australia captain Ricky Ponting, who said before the series he wanted Muralitharan to leave Australia without Warne's record, was unbeaten on 53 when he declared.

The 507 target would be a record by some distance - the West Indies' 418 against Australia at Antigua in 2003 is the highest winning chase for a team batting last in a Test.

And the mammoth target looked even larger when Vandort could only sky a simple catch to substitute fielder Rhett Lockyear at point as Sri Lanka slipped to 15-1.

The visitors were 23-1 lunch but they dominated the middle session, adding 116 runs without loss.

However, after tea Lee began to work Atapattu over and he eventually hooked a short ball to Phil Jaques at deep square leg.

And the next ball Lee produced a viciously swinging yorker to new batsman Jayawardene and the captain could only look on in horror as he failed to offer a shot and the ball swerved in to rattle his stumps.

Veteran left-hander Sanath Jayasuriya (33 not out) joined Sangakkara and the pair saw the visitors to the close.