It is given in the question that,

Radius of each circular disc $=r =1.5/2=0.75cm$

Height of each circular disc $=h=0.2cm$

Radius of cylinder $=R=4.5/2=2.25cm$

Height of cylinder $=H=10cm$

So, the number of metallic discs required is given by n

n $=$ Volume of cylinder / volume of each circular disc

$n=\pi {{R}^{2}}H/\pi {{r}^{2}}h$

$n={{\left( 2.25 \right)}^{2}}\left( 10 \right)/{{\left( 0.75 \right)}^{2}}\left( 0.2 \right)$

$n=3\times 3\times 50=450$

Therefore, $450$ metallic discs are required.