Calculating the Center of Mass & Force of Water on Half-Cylinder

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The center of mass of the solid half-cylinder is located at its geometric center due to its constant density. The discussion also addresses the force exerted by water on the lateral circular face of the half-cylinder, which is a challenging concept for some participants. Clarification is sought regarding the definition of a "lateral circular face" and the expectations for problem-solving contributions. There is a sense of frustration over the perceived lack of assistance in understanding the calculations involved. Overall, the thread highlights the need for clearer explanations and support in tackling physics problems related to fluid dynamics.
IntegrateMe
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A solid half-cylinder of radius 1 meters and length of 5 meters lies under 50 meters of
water at the bottom of a lake. The cylinder is made of a material of constant density d.

1. Find the center of mass.

I said that the COM will be in the center because there is a constant density.

2. What is the force exerted by the water on one of the lateral circular faces of the half
cylinder?

I'm having trouble understanding this part of the question. What exactly is a "lateral circular face?"
 
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Is there a reason why no one is helping me? Is it because I haven't "shown enough work" on a problem I don't know how to solve or even start?
 
Anyone?
 
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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