Let the edge of the cube be “x cm”. The minimum edge should be chosen such that the cube barely floats or is completely immersed. In this case, the weight of the water displaced would be due to the mass of the cube and the metal piece.

Given, mass of the metal piece,

Density of ice,

Density of water,

Volume of the cube, —————(1)

Therefore, the buoyant force would be, —————(2)

And the buoyant force is equal to the weight of the water displaced, —————(3)

Equating (1) and (2)

Using (1)

(ANS)

Therefore, the side of the cube should be around 17 cm.