A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg.

Let the minimum edge of the block = X cm 

The volume of the ice block =X³ cm³ =X³/10⁶ m³ 

Density of the ice = 0.9*1000 kg/m³ =900 kg/m³ 

The weight of the ice block =(X³/10⁶)*900 kg 

Total weight of the ice block and the metal piece = (X³/10⁶)*900+0.50 kg 

The force of the buoyancy = weight of the water displaced =(X³/10⁶)*1000 kg. (The volume of water displaced just before it sinks is equal to the volume of the ice cube = X³ cm³) 

In the given condition the weight of ice cube and the metal = force of buoyancy, 

→(X³/10⁶)*900+0.50 = (X³/10⁶)*1000 

→(X³/10⁶)*(1000-900) =0.50 

→X³ = 0.50*10⁶/100 =5000 

→X ≈ 17 cm