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## Homework Statement

Find the moment of inertia of a right circular cone of radius r and height h and mass m

## Homework Equations

I = ∫r

^{2}dm

V = 1/3*π*r

^{2}*h

## The Attempt at a Solution

Assume density is p

dm = p dv

divide both sides by dr

dm/dr = p dv/dr

dm/dr = p (d/dr * 1/3*π * r

^{2}*h)

so

dm/dr = p(2/3)*πrh

so:

dm = (2/3)pπrh dr

Sub that into the moment of inertia equation

∫(2/3)pπrh dr = I

I = (1/3) pπr

^{2}h

p = m/v

I = (1/3)(m/v)πr

^{2}h

I = v*(m/v)

I = m

What am I doing wrong?