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 $79.04cm$.