How can you find the mass of a mountain?

Answer 1

Density times volume equals mass.
To find the volume: Let's assume that the mountain has a somewhat conic shape. The volume is roughly (1/3 times pi times the radius of the base squared times the height of the mountain). So if a mountain is five miles wide at the base and 1000 feet high, the volume is (1/3 x 3.14 x 13,200 x 1000) about 14 million cubic feet, which is about 391 billion cubic centimeters.
Now for density: most mountains are made largely of granite, which has a density of 2.7 grams per cubic centimeter. So multiply the volume by the density of granite. In the example above, the volume times the density is 1056308992089.12 grams: about a million tons.

This is a very, VERY rough approximation. If you wanted to be more exact you'd have to take the topography into account, the actual shape of the mountain, etc etc. But still: volume times density equals mass, and most mountains are made of granite, so their density is about 2.7 grams per square centimeter. The hard part is finding the volume.