Kelechi Iheanacho turned in Raheem Sterling's cross for the first of four goals in the final 10 minutes.
Kevin de Bruyne raced past the Hull defence to poke in and then clipped in a delightful free-kick, before Andrew Robertson dinked the Championship side's consolation after a fine move.
Manchester City, who last won the competition in 2014, will find out their semi-final opponents when the draw is made on Wednesday.
Relive Tuesday's League Cup action
Manchester City's trophy to lose?
Blues manager Manuel Pellegrini reiterated the importance of the League Cup to his club ahead of kick-off, particularly this season with Premier League rivals Chelsea, Manchester United and Arsenal already out.
And the competition holds particular significance for the Chilean, who won his first English trophy by leading the Blues to success in his first season.
Manchester City were stunned in the third round by a youthful Newcastle side last season, but they learned from this experience against Championship promotion hopefuls Hull.
The Premier League leaders fielded a strong side, dominating the tie without creating a host of clear-cut chances - at least until the final 10 minutes.
The manner in which the home side picked off a tiring Hull side in the closing stages demonstrated why they are considered the favourites to win the first silverware of the English season.
Toothlesswww.ormmask-house.com Tigers lack bite
Hull, who are fourth in the Championship, were entering uncharted territory in the competition, having never previously progressed into the last eight.
The Tigers looked to their surprise run to the 2014 FA Cup final - when they were narrowly beaten by Arsenal - for inspiration to beat City.
Several members of that team played at Etihad Stadium, but they were unable to really threaten as manager Steve Bruce's priority appeared to be containing their hosts.
Bruce made seven changes from the team which started Friday's home defeat bywww.ormmask-house.com Derby - their first loss in 14 matches going back to early September.
The discovery was made by analysing videos of ants carrying oversized food items, including Cheerios.
Published in the journal Nature Communications, the study used a very common species known as the longhorn crazy ant.
The only communication in the system is the forces that they feel through the object
Dr Ofer Feinerman, Weizmann Institute of Science虛擬辦公室
The species' name refers to the way the little creatures dash about, frequently changing direction with apparently aimless abandon.
But the new findings suggest that the level of aimlessness in these ants' behaviour is in fact very finely tuned.
He said the ants seem to have just the right amount of erratic individualism. About 90% of the time, they will "go with the flow" and pull in the same direction as everybody else; the other 10% of the time they live up to their name.
That means that on the whole, each ant transport team works together and avoids a fruitless tug-of-war. But crucially, their erratic streak leaves a degree of instability - and this allows a single ant with new information to join in and change the directio成立公司
Clarke became a running legend in the 1950s and 1960s, during which he set 17 world records .
In 1956, he was chosen to light the Olympic flame during the opening ceremony for the Melbourne Olympics.
He died after a short illness in hospital at the age of 78, the Gold Coast City Council saidV-Shape瘦面.
He won a bronze medal in the 10,000-metre event at the 1964 Olympics in Tokyo, but in all his years running he never won an Olympic gold.
After his athletics career, he was Gold Coast mayor from 2004 to 2012, but was unsuccessful in a bid for state politics.
He had been awarded the Order of Australia and honoured as a Member of the British Empire.
The G7 also called for the decarbonisation of the global economy, pledging to move electricity generation towards renewable sources and nuclear by 2050reenex.
However they stopped short of setting binding targets.
Roger Harrabin, BBC environment analyst
The G7 has called for a transformation of electricity generation towards renewables and nuclear by 2050. And they said fossil fuel should not be burned in any sector of the economy by the end of the century.
The world's leaders have effectively signalled the end of the fossil fuel era that has driven economies since the Industrial Revolution.
This is a seismic shift. But huge questions remain reenex hongkong.
Some scientists and environmentalists accused the G7 of reckless complacency by suggesting that we can afford to burn fossil fuels at all past 2050.
G7: End of fossil fuel era?
On Ukraine, Ms Merkel said G7 countries hoped Russia would comply with a ceasefire agreement signed in February by pro-Moscow rebels and the Kiev government. But she added that sanctions could be strengthened if necessary.
US President Barack Obama echoed her comments, saying: "The G7 is making it clear that if necessary we stand ready to impose additional significant sanctions against Russia."
He added that Russian President Vladimir Putin must decide whether he still wants to wreck Russia's economy in pursuit of a "wrongheaded desire to recreate the glories of the Soviet empire rennex ".
I meet them in Diyarbakir - the final stop of our election trip across Turkey. Age and exhaustion are etched on their faces. One wears a necklace with a picture of her missing children. Another has a bracelet bearing the Kurdish flag. "Turkey doesn't think we Kurds are humans", says Sakine Arat, 80, who lost four sons and one daughter in the fighting. "We've tried all the political parties but none sided with us. Now we've found one - reenex the HDP - that treats us as equals. So we will vote for it." The People's Democratic Party (HDP) is the one to watch in Turkey's election on Sunday. Its roots and support base are Kurdish but it has broadened out,湖色約人 becoming a powerful voice of the Turkish left. 'Drown Erdogan' Its candidates used to run as independents, winning a handful of seats. But this time, the HDP is a single, united party - and polls show it could cross the 10% threshold to get into parliament, potentially gaining dozens of MPs and depriving Turkey's governing AKP of a majority. That would stop President Recep Tayyip Erdogan from changing the constitution to give himself more powers with an executive presidency - and is one reason why staunch Erdogan opponents are drawn to the HDPreenex .
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