cone area spherical coordinates

What is the formula for the cone in spherical coordinates?
If we divide by z=ρcosϕ, we obtain a formula for ϕ in terms of Cartesian coordinates √x2+y2z=tanϕ. where C=1/tanϕ, which is indeed the equation for a cone.
What is the area of a cone in cylindrical coordinates?
In cylindrical coordinates, the infinitesimal surface area is dA=sdθdz.
Using the straight line equation which gives s=Rh(h−z), I obtain A=πRh.
What is the area of a spherical coordinate?
The formula for surface are of a sphere is 4 times pie times the square of its radius.
At first we need to split the surface in infinitesimal areas.
In Spherical Coordinate System a point on the surface can be represented as (r, θ, ϕ). θ is called the Polar angle and ϕ is called the Azimuthal angle.
So that the equation of a cone with vertex at the origin is of the form, ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy = 0, which is a homogeneous in x, y and z.
Note that the converse of this theorem is also true.
The coordinates of the origin satisfy the equation (9.10).

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