A metallic wire of density d floats horizontally in water. The maximum radius of the wire so that the wire may not sink is (surface tension o water = T)

If the weight (mg) of the wire is balanced by the surface tension force (T) operating on it, the wire will not sink.
Thus, the cable will experience zero net force.

$\therefore \mathrm{mg}=\mathrm{T}\cdot 2l$

$\left({\mathrm{\pi r}}^{2}l\mathrm{d}\right)\mathrm{g}=\mathrm{T}\cdot 2l$

$\mathrm{r}=\sqrt{\frac{2\mathrm{T}}{\mathrm{\pi dg}}}$

Hence the correct answer is $\sqrt{\frac{2\mathrm{T}}{\mathrm{\pi dg}}}.$