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We typically say:

The roof of the cave is 100m tall.

But I just saw in Cambridge Dictionary:

The roof of the cave is 100m up.

Explain me the usage.

Thank you.

NOTE: I have been taught up as an adjective is used to talk about increase in price, level, amount etc.

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1. The roof of the cave is 100m tall.

This means that the roof itself is 100m tall.

I'm not familiar with cave roofs, so I don't know if there are features by which you can judge the bottom part of a cave's roof and the top part of a cave's roof. (Or even, if if I'm honest, what a cave roof would actually consist of, aside from its vertical termination with some kind of horizontal structure.)

If you were talking about the roof of a house, it would be the part that is located above the regular rooms, the part that protects everything below it from wind, rain, and snow. A traditional house roof is sloped, and its construction extends beyond the vertical walls that it rests upon. (Of course, not all house roofs are constructed that way.) Let's say that the height of a typical roof is 3 metres, and that with a two-storey house it sits on top of 6 metres of vertical walls.

100 metres seems to be an excessive height for any kind of roof, even a cave roof. Therefore, I certainly don't think that we "typically" use this phrasing.


2. The roof of the cave is 100m up.

This is talking about how much higher the roof is than you (or something), relative to your current position. For a house, this would make no sense—but it would for a 30-storey apartment building if you were standing on the ground and looking skyward.

The use of up here is directional. (It has a large number of different senses, each of which is contextual.) I could point my finger into the air and say, "Look at that roof up there!"

Unlike in the first sentence, the roof itself could still be a much shorter 3-metres tall, sitting on top of the main walls of the cave.

I would say that this is the more common phrasing of the two, and the one that makes the most sense.

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Think of that use of up as not a moving increase, but rather a relative description. The example from the Cambridge Dictionary used up to describe where the roof is in comparison to the floor of the cave. Essentially it uses up without explaining the full extent of what the roof is up from, where a better way to express the height of the roof would be:

The roof of the cave is 100m above the floor. (Or ground, but that phrasing is irrelevant.)

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