This question is an exact duplicate of:
When we rotate a right angled triangle about its perpendicular we get a solid cone. For a right-angled triangle the centre of mass is at its centroid i.e., at $(\frac h3, \frac b3)$. If we consider a solid cone to be made up of many right-angled triangles, the centre of mass should be at a height of $\frac h3$ from the base whereas it is at $\frac h4$ from the base for a solid cone. I have obtained the proper answer through integration but I am unable to figure out where I am going wrong in this logic. Kindly point out where I am going wrong.