ANSWERS: 6
• It would depend on how high it was, and what it was composed of.
• 1) with or without the trees? 2) "A simple approximate way is to assume the density of rock is about 2.0gm/ml. You can choose another density if you want. Assume the mountain is a cone and use the formula for the volume of a cone to compute the total mass. Mountains are in fact "weighed" experimentally using sensitive gravimeters -- instruments that measure the local gravitational constant. This is done both on the ground and on satellites. From the variation of the local gravitational constant the mass of the mountain can be determined by more sophisticated numerical techniques." Source: http://www.newton.dep.anl.gov/askasci/env99/env238.htm
• a mountin dew weights 16 ounces
• My estimate is in the range of billions of tons. A model that I've used before is what I remember about the composition of the Great Pyramids of Egypt. IIRC one of them is composed of 2,300,000 stones weighing 2 1/2 tons each for a total of 5,750,000 tons. I think that pyramid is about 400 feet tall so a 4000 feet mountain of an approximately pyramidal shape would be about 1000 times heavier or 5,750,000,000 tons.
• Let's look at the question. We have a mountain 10,000ft tall. If we assume a roughly conical shape (it's out there all by itself and not part of a mountain range), we need to know the diameter of the base to find the approximate volume. If you look mountains are usually a lot broader than they are tall which makes sense: If the mountain were tall and narrow then weathering would crumble the sides of the mountain away and after a few million years all you'd have is a very broad and very low rubble pile. There has to be enough material to support the rocks on top to minimize this. So let's say as a first approximation that our mountain is twice as broad as it is tall, which makes it 20,000 feet at the base. The volume of a cone is 1/3 x pi x (D/2)^2 x h where D is Diameter and h is height. pi is the univeral constant 3.141529 etc. etc. With a caculator we can find the volume as 1.0471975511965977461542144610932e+12 cubic feet!!! Now we need to know the density and while mountains are made of many natural substances let's be simple about it and assume it all good old granite, which is 2.8 grams per cubic centimeter. You'll notice we have a problem with our units, where the volume is in English units and the density is in European. Fortunately the Internet abounds with conversion calculators so we know that 1 cubic centimeter = 0.000 035 314 667 cubic feet and 1 Gram = 9.84206527611061E-07 Tons - Long So again to our (hard pressed!) calculator and we come up with a final weight for our hypothetical, squat, 10,000' tall granite mountain of 8.1718E+17 tons Or thereabouts. To put it in perspective if you drilled under said mountain and buried the biggest nuclear warhead ever made underneath and set it off, the mountain would barily quiver and there would be no noticeable release of radiation or heat to the envirnment. This answer is not guaranteed accurate; feel free to check my math and correct me where I'm wrong.
• Hmm...may as well add my own thoughts here: While Mountains can have 45 degree slopes, just checking some well-known mountains on Google Maps they tend to average closer to maybe 25 degree slopes: http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=mt+rainier&sll=27.992317,86.943011&sspn=0.018455,0.02605&ie=UTF8&ll=46.851622,-121.768856&spn=0.054238,0.104198&t=p&z=13 This means the base of the mountain is 4x the height; the radius is 2x the height. So using the cone equation like everyone else (pi/3 * r^2 * h) we have weight = density * pi/3 * (2h)^2 * h As others have linked to, density is in the 2.0 to 2.7 grams per cubic centimeter range, so 2000-2700 kg per cubic meter range. Fortunately for us, this density makes our equation roughly... weight = 10,000 * h^3 Where h is the height in meters, and the weight is in kilograms. Mountain height ranges from about 500 meters to 5000 meters (see: http://en.wikipedia.org/wiki/Mountain), so... 500 meters -> 10^12 kg 1000 meters -> 10^13 kg 2000 meters -> 10^14 kg 5000 meters -> 10^15 kg (If you want the result in tons, divide by 1000).

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