City of Montreal plans for starting a new ski resort by building a mountain out of landfill trash. The shape can be approximated by a right circular cone of altitude 1,100 with a base diameter of 12,000 . The parametric equation of a right circular double cone with vertex at 0 is given as ( ) 2 = 2+ 2 2 , where is the ratio of the radius with the height of the cone.

Q:) In reality, with the passage of time the trash at the bottom would become more compact than that above it due to sinkage. At a particular time, samples were taken at various heights and changes in density were measured. The peak of the mountain still showed the initial density of 400 / 3 , but every 100 lower the density increased by 400 / 3 . What would be the total weight of the mountain in at this particular time?

mass= density(x, y, z) dV Find total mass