Struggling with Statics Problems? Need Help with Equations?

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The discussion revolves around a user seeking assistance with statics problems, expressing difficulty in identifying the correct equations to solve them. The user admits to having made little progress and feels lost on how to approach the problems. Clarifications are made that the issues pertain to statics, not statistics or geometry. Participants emphasize the importance of understanding the fundamental principles of statics to tackle the equations effectively. The conversation highlights the need for guidance in applying the right methodologies to solve statics problems.
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I would like to know if anyone could help me with the attached statics problems. I've worked on these for quite sometime and haven't been able to figure them out. Thanks
 

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what work have you done so far? And these are geometry problems not statistics.
 
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I haven't really done much work at all the biggest problem I have is getting the right equations. On some of them I just don't know where to go at all. Also these are statics problems no statistical problems, thanks for your help.
 
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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