$A$ person is sitting in a boat floating in a lake. This person fills a bucket of water from the lake and puts it in the boat. Will the water level in the lake go down? Explain.

(N/A) No,the water level in the lake will not change.
According to Archimedes' principle,the weight of the water displaced by the boat is equal to the weight of the boat and the person.
When the person takes a bucket of water from the lake,the weight of the water removed is equal to the weight of the water displaced by the bucket when it was submerged.
When the bucket is placed inside the boat,the total weight of the boat increases by the weight of the water in the bucket.
This additional weight causes the boat to sink slightly deeper,displacing an amount of water equal to the weight of the water in the bucket.
Since the volume of water added to the boat is exactly equal to the volume of water removed from the lake,the net change in the water level of the lake is zero.