This is not properly formed because of three reasons,

1) Shape of the object should be precisely stated, it should be given as right circular cone instead of just a cone.

2)Distribution of particles within the object should be mentioned, it should be given as uniform otherwise density need to be given as a function.

3)Without knowing the numerical values of dimensions we can not assume centre of mass is at the same position of centre of gravity. Therefore the correct way is to ask position of centre of mass.

1)When f(x) and g(x) are given as expressions you can just replace x in f by g(x) and it gives an expression for f(g(x)).

Let f(x) = x²  , g(x) =  √(x – 1)                                      f(g(x)) = x – 1 and f(g(0))= -1

2)When domains of f and g given you can find the range of g , and f(g(x)) exists if the range of g is a subset of domain of f  . In this case domain of f(g(x)) is same as the domain of the function g.

In the previous example if domain of f given as all real numbers and domain of g as real numbers not less than 1 ,  range of g is set of positive real numbers including 0 and it is subset of domain of f . Therefore f(g(x)) can be defined. But f(g(0)) can not be defined because 0 is not in the domain of the composite function. Since range of f is not a subset of domain of g ,  g(f(x)) can not be defined.

3)If you are asked to find f(g(x)) with it’s domain without giving domains of f and g , you need to restrict the domain of g in order to make range of g to be a subset of domain of f.

Let f(x) = √(x -1) , g(x) = x²                                       here you need to restrict domain of g to             (-∞ , 1] ∪  [ 1 , ∞ ) in order have range of g that is [ 1  ,  ∞ ) as a subset of domain of f.

Hope this answer would be sufficient to get the clear picture of the issue. I think better way to get this fully understood is to practice for few more problems.  Appreciate your suggestions regarding this answer. Because of a system error sometimes your reply can be taken as another answer.