To increase the density of a hollow lead ball filled with water, you would compare the two options provided:
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Remove the water and melt the ball into a solid sphere: This option would definitely increase the density. A solid lead sphere would have a uniform density of lead, which is significantly denser than water. The density of lead is approximately 11,343 kg/m³, whereas the density of water is only about 1,000 kg/m³. Thus, converting the hollow lead ball into a solid lead sphere would lead to a much higher overall density.
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Remove the water and replace it with oil: While this option would also increase the density compared to having water inside (depending on the type of oil, the density typically ranges from about 700 kg/m³ to 950 kg/m³), it would not reach the density of solid lead. The overall density of the hollow ball would be a weighted average based on the lead structure and the oil inside, which would still be less dense than solid lead.
In conclusion, if the goal is to maximize the density of the hollow lead ball, the best option is to remove the water and melt the ball into a solid sphere.