Shown in the figure is a hollow ice-cream cone (it is open at top)....

It can be assumed as several parts of discs having different radius, so

$I = ∫ dl = ∫ dm\left({r}^{2}\right)$

From diagram

$\dfrac{r}{y} = tan\text{\theta} = \dfrac{R}{H}$

$r = \dfrac{R}{H} \cdot y$

$dm = \text{ρ}\left(\text{\pi}{r}^{2}\right)dy$

From equation (i), (ii) and (iii)

$I = \dfrac{M{R}^{2}}{2}$