When a floating ice cube melts, the volume of water displaced: 

According to Archimedes' principle, a buoyant force equal to the weight of the fluid that the body displaces acts on a body at rest in a fluid to push it higher.

Some of the water will be displaced by the floating ice.

From Archimedes' principle, ${\mathrm{F}}_{\mathrm{B}}={\mathrm{\rho }}_{\mathrm{water}}\times \mathrm{g}\times {\mathrm{V}}_{\mathrm{ice}} -\left(1\right)$

Weight of the displaced fluid (water) $= \mathrm{mg} = {\mathrm{\rho }}_{\mathrm{water}}\times {\mathrm{V}}_{\mathrm{displaced} \mathrm{water}}\times \mathrm{g} -\left(2\right)$

For an object to stay afloat, the forces acting on it must be balanced $\mathrm{Now}, \left(1\right) =\left(2\right)$

$$\begin{gathered} {\mathrm{\rho }}_{\mathrm{water}}\times \mathrm{g}\times {\mathrm{V}}_{\mathrm{ice}} = {\mathrm{\rho }}_{\mathrm{water}}\times \mathrm{g}\times {\mathrm{V}}_{\mathrm{Displaced} \mathrm{water}} \\ \Rightarrow {\mathrm{V}}_{\mathrm{ice}} ={\mathrm{V}}_{\mathrm{Displaced} \mathrm{water}} \end{gathered}$$

Hence, option C is correct.