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 $1600$