Electric field due to a line charge, surface area

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To find the surface charge density of a uniformly charged circular disk, the formula S = charge/area is used. The correct area for one face of the circular disk is πr², not the circumference 2πr. The discussion clarifies the importance of using the correct area calculation for accurate results. Understanding these fundamental concepts is crucial for solving problems related to electric fields and charge distributions. Proper application of formulas is essential in physics calculations.
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Homework Statement


A charge distributed uniformly over 1 face of the circular disk, find the surface charge density ?


well i know density for surface charge is S= charge/area, the area for face of 1 circular disk is what ? 2pir ?
 
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area of a circle is pi*r^2
what u have is the circumference
 
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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