Center of mass and density?

Question

A cylindrical concrete silo is 4 m in diameter and 33 m high. It consists of a 6000 kg concrete base and 38000 kg cylindrical concrete walls. Neglect the thickness of the silo walls and base.

(a) How high off the ground is the center of mass of the silo when it is empty?

(b) How high off the ground is the center of mass of the silo when it is two-thirds full of silage whose density is 820 kg/m3?

Answer 1

What is the geometry if the concrete base. Is it a ring or a rectangular slab?

In general sum the moments about say x or y axes (assuming that it is symmetrical in x and y)
Then divide the result by the sum of the masses and you will get your z-centroid.