How can we find the center of mass of a solid cone?

[Nimarjeet Bajwa]

Homework Statement

Find the center of mass of a solid cone taking a hollow cone as an element. given that both coens are made of same material

Relevant Equations

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is this method even possible? anyways here is my attempt

Step1) y= 2H/3 ( H is the height of the cone)

step 2) we take the density (ρ)= 3M/π R² H.

The problem i am facing is to Find "dm"

 

[haruspex]

Homework Statement: Find the center of mass of a solid cone taking a hollow cone as an element. given that both coens are made of same material
Homework Equations: -

is this method even possible?

Yes.
Consider a nested stack of hollow conical shells each of thickness dr. Find the mass and mass centre of each (measured from the common base).

 

[Nimarjeet Bajwa]

Yes.
Consider a nested stack of hollow conical shells each of thickness dr. Find the mass and mass centre of each (measured from the common base).

should we also take a height of every hollow cone as "dh" ?

 

[haruspex]

should we also take a height of every hollow cone as "dh" ?

The heights will not be infinitesimals, so dh would be inappropriate.
If the radius of one of these hollow cones is r, what is its height?