Uncertainty of the function? My answer is a bit different

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The discussion centers on a homework problem involving the uncertainty of a function. A participant points out a potential error in the calculation, specifically questioning why δz was divided by z while δx + δy was not divided by any value. This discrepancy suggests a need for a review of the formula used in the solution. The conversation emphasizes the importance of consistency in applying mathematical principles to uncertainty calculations. Overall, the thread highlights the necessity of careful analysis in problem-solving.
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Homework Statement



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Homework Equations

The Attempt at a Solution


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The answer is different though,
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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