Shown in the fig. is a hollow ice-cream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is :

From the vertex, along curved surface go to y and take a strip of thickness dy​and radius x.Mass of this strip = dm=mass on CSACSA×area of strip⇒dm=MπRR2+H2×2πxdx​Also, from similar triangles, xy=RR2+H2 I=   dm  x2  =MπRR2+H2   2πx3 dy​I=2MRR2+H2×R3R2+H232×y440R2+H2=MR22