According to the question,

Diameter of the coin $=1.75cm$

Then, its radius $=1.74/2=0.875cm$

Thickness or the height $=2mm=0.2cm$

As we know that,

Volume of the cylinder $\left( {{V}_{1}} \right)=\pi {{r}^{2}}h$

$=\pi {{0.875}^{2}}\times 0.2$

And, the volume of the cuboid $\left( {{V}_{2}} \right)=11\times 10\times 7c{{m}^{3}}$

Assume the number of coins needed to be melted be n.

Then, we have

${{V}_{2}}={{V}_{1}}\times n$

$11\times 10\times 7=\pi {{0.875}^{2}}\times 0.2\times n$

$11\times 10\times 7=22/7\times {{0.875}^{2}}\times 0.2n$

On solving we get, $n=1600$

Therefore, the number of coins required are $1600$