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The density of water depends on its temperature, but as you didn't give a temperature and for simplicity sake here we will take the density of water to be 1g/cm3.

We will also consider the density of the swimmer to be uniform, else we will have to get into a serious discussion about anatomy.

Lets convert 150 lbs. into grams --->

150 lbs *453.59237 g/lb = 68038.8555 grams

In order to counter this mass 68038.8555 grams of water is going to have to be displaced. This will be a volume of 68038.8555 cm3.

95% of the swimmers volume = 68038.8555 cm3

so

.95x = 68038.8555 cm3. x= 71619.8479 cm3 where x is the total swimmer's volume.

density is Mass/Volume

so

Swimmer's density is 0.949 g/cm3 or 0.949 g/ml

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How is the density of a floating object relate to the density of the fluid it is floating in?

If an item floats, Then it is less dense than the liquid it floats in. One can prove this using bernoulli's equation. To determine the weight of the floating object, take the volume of water displaced by the portion of the object below the fliud surface then multiply that by the density of the fluid. This process gives you the bouyant force on the floating object and therefore the weight. Then take that weight and divide it by the total volume of the. Object to get its density. Also note that if an item is suspended below the surface but. Above the bottom of the fluid body, then the item and fluid have equal density. If the item sinks to the bottom it has higher density than the fluid.


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The size of the surface will affect the buoyant force acting on the object, with larger surfaces experiencing greater buoyant forces. The mass of the object will influence how easily it can displace water, affecting its ability to float. A larger mass may sink if it cannot displace enough water to counteract its weight.


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