Final answer:
According to Archimedes' principle, the children on the raft will not get their feet wet.
Step-by-step explanation:
According to Archimedes' principle, an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. To determine if the children will get their feet wet, we need to compare the weight of the raft and the children with the weight of the water displaced by the raft and the treasure chests.
The total weight of the raft and the children is the sum of their individual masses, which is 32 kg + 35 kg = 67 kg. The total weight of the treasure chests is 2 * 25 kg = 50 kg.
The volume of the raft can be calculated as its length multiplied by its width multiplied by its height, which is 1.8 m * 2.0 m * 0.18 m = 0.648 m³.
The volume of each treasure chest is given as 0.021 m³.
The density of the wood used to make the raft is 560 kg/m³.
Now, we can calculate the weight of the water displaced by the raft and the treasure chests as the product of the volume and the density of water, which is 1000 kg/m³.
The weight of the water displaced by the raft is 0.648 m³ * 1000 kg/m³ = 648 kg.
The weight of the water displaced by the treasure chests is 2 * 0.021 m³ * 1000 kg/m³ = 42 kg.
The total weight of the water displaced is 648 kg + 42 kg = 690 kg.
Since the weight of the raft and the children (67 kg) is less than the weight of the water displaced (690 kg), the raft will not sink and the children will not get their feet wet.