We can assume that the radius of the cone is the same as the crown, however, how can we measure the height of the cone?

Notice the two similar triangles.

Can we assume that the shape of the cone is similar to the mountain?

If their slopes are the same, then we can construct the following proportion.

 

             (h)/(H) = (r)/(R-r)

By multiplying both sides of the proportion by "H", we have an expression for "h" in terms of real and measurable quantities.

Substituting this expression for "h" into our volume formula produces a new equation.           

V = (p r³H) / 3(R - r)

Assuming these measurements:    r = 350 m,  R = 2530 m, H = 1800 m

Calculate the volume of the cone.

If the density of the soil material is 3/4 ton per cubic meter, what is the weight of the cone that was displaced?

How can we proceed to approximate the force of the volcano?