A bucket of water is heavier than a bucket of snow when both are of the same size. This is because water is denser than snow; snow contains a significant amount of air, which makes it lighter. Thus, even a full bucket of snow will weigh less than a full bucket of water.
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one tenth of a gallon
Well, if I am correct the water in the bucket stays in there because of inertia and centripetal force. The water wants to come out of the bucket but inertia prevents the water to come out of the bucket. That is all I know I don't know how centripetal force helps the water stay in the bucket though. Hoped this helped you a bit.
The bucket full of water because liquids heat up faster than solids.
It depends on the volume of the bucket.
How large is the bucket? I would suggest pouring water in to find out.