An ice block with a piece of lead embeded in it floats in water. If ice melts the water level

If r1 is the density of the lead piece of volume v, the volume of water displaced by the ice block and the lead piece while floating is Vw = (V–v) r1 + v r1. When the ice melts, the lead piece sinks in water since r1 is greater than the density of water. The water produced by the melted ice has the volume (V-v) r1 and the volume displaced by the lead piece is v. So, the total volume of the water produced by ice and that displaced by the lead piece is V w1 = (V–v) r1+ v r1< V w. So, the water level goes down.