Laplace operator in spherical coordinates

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The discussion revolves around the confusion regarding the labeling of images related to the Laplace operator in spherical coordinates. Participants emphasize the importance of clear labeling to avoid misunderstandings. A link to the Wikipedia page on the topic is provided as a resource for clarification. There is also a note about the readability of images, specifically advising against posting them sideways. Clear communication and proper formatting are highlighted as essential for effective discussion.
physicss
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Homework Statement
Hello, I had to calculate ∆r and ∆Theta,phi. Is the answer on the second picture correct?
Relevant Equations
∆r, ∆Theta,phi
AF8CF310-EAA1-49D5-849E-36C87E749D71.jpeg
36C3B8DA-8751-43C9-8175-DFC4BDC35448.png
 
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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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