The solid cylinder of length 80cm and mass M has a radius of 20cm ....

$I = \dfrac{M{r}^{2}}{2} + \dfrac{M{L}^{2}}{4} = \dfrac{\left(ρ\pi{r}^{2}L\right){r}^{2}}{2} + \left(ρ\pi{r}^{2}L\right)\dfrac{{L}^{2}}{4}$

$= ρ\pi{r}^{2}L\left(\dfrac{{r}^{2}}{2} + \dfrac{{L}^{2}}{4}\right)$

$⇒ ρ = \dfrac{I}{\pi{r}^{2}L\left(\dfrac{{r}^{2}}{2} + \dfrac{{L}^{2}}{4}\right)}$

On putting the values, we get $ρ = 1 . 49 \times {10}^{2}kg{m}^{- 3}$.