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Customers wait in line behind an Apple iPhone 6 Plus on display at SoftBank’s Omotesando store during the sales launch of the iPhone 6 and iPhone 6 Plus in Tokyo Sept. 19, 2014.Yuriko Nakao/Bloomberg

Even by Apple Inc.'s lofty standards, it was an astounding quarter.

Supercharged by record iPhone sales, the world's biggest technology company posted record quarterly earnings on Tuesday – in the process demolishing analysts' expectations.

"Today we're reporting a historic quarter," Apple CEO Tim Cook said in an investor conference call. "Interest in Apple products is at an all-time high."

For the three months that ended on Dec. 27, Apple posted record revenue of $74.6-billion (U.S.) and record quarterly net profit of $18-billion, or $3.06 a diluted share.

Analysts had expected, on average, revenue of $67.69-billion and earnings of $2.60 a share, according to Thomson Reuters.

More than any other product category, the new, larger-screen iPhones were perhaps most responsible for Apple's record first quarter. On average, according to Mr. Cook, the company sold more than 34,000 iPhones an hour, 24 hours a day, every day during its last quarter.

"This volume is hard to comprehend," he said.

For years, especially under the leadership of late CEO Steve Jobs, Apple resisted the urge to significantly alter the size of its iPhone screens – even as rivals such as Samsung ate away at Apple's smartphone market share by offering a vast array of devices at different price tags and screen sizes.

However, that strategy came to an abrupt halt last fall, when Apple unveiled its newest generation of smartphones, the iPhone 6 and iPhone 6 Plus. The larger-screen, higher-priced iPhone 6 Plus proved a huge hit with customers, some of whom may have previously seen fewer compelling reasons to upgrade from the older generation of the hyper-popular smartphone line.

In all, Apple sold 74.5 million iPhones in the quarter, roughly 10 million more than what the Street expected.

The iPhone effect could be readily seen across virtually every financial metric. Demand for the new phones was especially strong in China, Apple's most important overseas market. Over all, international sales accounted for about 65 per cent of the total.

Perhaps most importantly, iPhone sales also helped Apple's gross margins, which have either moved sideways or declined in the past few years, as the smartphone industry becomes more commoditized. Apple's gross margins in the last quarter were 39.9 per cent, well ahead of both analyst expectations and the same quarter last year, and higher than they have been since the fourth quarter of 2012.

However, the hugely successful quarter could create more challenges down the road for Apple. As Mizuho Securities analyst Abhey Lamba said in a note to clients shortly before Apple announced its results on Tuesday, the huge upgrade cycle created by the new line of iPhones could make the same period next year look disappointing by comparison.

"While current upside is widely expected, the downside risk to estimates is not reflected in the stock price. Apple needs to attract [40 million to 50 million] net new iPhone users per year to sustain growth, which could be challenging."

The next two quarters are also likely to be pivotal for the company. As the launch-cycle euphoria of the iPhone 6 wears off, investors and analysts will be keeping a close eye on Apple's newest ventures – specifically, its new smartwatch and mobile payments platform – to see whether the company can create another truly new billion-dollar business.

"My expectations for [the new Apple smartwatch] are very high," Mr. Cook said. "I'm using it every day, and I love it, and can't live without it."

For the current quarter, Apple's guidance of $52-billion to $55-billion in revenue was largely in line with analysts' expectations.

After dipping about 1 per cent so far this year, Apple shares jumped almost 5 per cent in after-hours trading on Tuesday.