What is the weight of Mt. Fuji? I see 100 billion tons a few places. What do you think?

Question

It's said to be a perfect cone, but it has a caldera at the top two kilometers wide. It's mostly basalt, but not entirely solid because it's the product of many eruptions -- maybe more like compacted crushed basalt -- I'm not sure.

Please, if you can, include numbers and sources. Thanks.
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Below is one calculation a friend attempted. Is it close to accurate? If not, what's flawed? I can see, for one, that he's not taking the caldera into account.
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Mt. Fuji is made almost entirely of basalt. I figured out how much a cubic meter of solid basalt weighs (3011 kg/cu.M).

Mt. Fuji is 3,776 meters tall and about 11,300 meters across at the base.

I then figured out the volume of Mt. Fuji. (area of base * height)/3 or…126,224,799,813 cubic meters.

So the Basalt in Mt. Fuji weighs nearly 380,062,872,237 metric tonnes.

Good point about the base-to-top height: I'm consistently seeing Fuji's elevation from sea level is 12,387 feet above sea level. There is a city at the base listed at 2,140 to 2,800 feet above sea level (http://www.answers.com/topic/fujiyoshida-yamanashi). So, the actual base-to- top height of Fuji is probably closer to 10,000 feet.

Answer 1

Nick is right. But I think can assume Fuji's base to be sea level since it is on an island and not an interior mountain range such as the Alps and the Himalayas.

And Fuji is a volcano, though it hasn't erupted in a few hundred years.

V = 1/3 π r^2 h
...= 1/3π(3776)(11,300/2)^2
...= 126,200,000,000 m^3
...= 1.262E11 m^3 (to 4 sig figs...further precision is meaningless)

mass = 3011 * 1.262E11
...= 3.801E14 kg (again to 4 sig figs)
...= 3.801E11 metric tons

Close enough to your calcs...but be careful of sig figs. Also, considering the irregularity of the conical volume of the mountain, I would think 1 sig fig would be sufficient:

4E11 metric tons

Answer 2

I think you are mostly correct in your estimate, except for one thing.

Most mountains as distinct entities do not start at sea level, though their heights are quoted from sea level. For instance. Everest sits on the Tibetan plateau, and the distinct moutain you see is only about 17,000 of the 29,000 feet. Same with the famous peak of the Matterhorn - what you see is only about half the height of its total height from sea level.

So, you would have to estimate the cone of Fuji from its base height. I would imagine that could be up to 1000 m above sea level.

Otherwise, volcanoes are the best samples to take, as you can apply the formula for the volume of a cone, as you rightly did.