According to the question,
Diameter of the solid cylinder $=2cm$
Length of hollow cylinder $=16cm$
The solid cylinder is recast into a hollow cylinder of length $16cm$, with external diameter of $20cm$ and thickness of $2.5mm=0.25cm$
As, we know that,
Formula of volume of a cylinder $=\pi {{r}^{2}}h$
Radius of the solid cylinder $=1cm$
Then,
Volume of the solid cylinder $=\pi {{1}^{2}}h=\pi hc{{m}^{3}}$
Now assume the length of the solid cylinder as h
Volume of the hollow cylinder $=\pi h\left( {{R}^{2}}-{{r}^{2}} \right)$
Thickness of the cylinder $=(R–r)$
$0.25=10–r$
Then, the internal radius of the cylinder is $9.75cm$
Volume of the hollow cylinder $=\pi \times 16\left( 100-95.0625 \right)$
So,
Volume of the solid cylinder $=$ volume of the hollow cylinder
$\pi h=\pi \times 16\left( 100-95.06 \right)$
$h=79.04cm$
Therefore, the length of the solid cylinder is $79.04cm$.