Finding the Percentage of a Sphere Immersed in Water

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To find the percentage of a sphere immersed in water, consider the relationship between the densities of the sphere and water, similar to how ice floats about 90% submerged. The density of the object divided by the density of the fluid gives the percentage of immersion. In constructing a free body diagram, it is essential to include both the buoyant force and gravitational force, as they relate to the densities involved. The buoyant force indeed connects to the densities, allowing for the calculation of the percentage of the sphere submerged. Understanding these principles will help solve the problem effectively.
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So I'm in a general physics class and the teacher asked us to find the percentage of a sphere immerses in water and I can't seem to figure out how to find the percentage. I was wondering if there's an equation to use or what to find the answer. Thanks.
 
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Welcome to PF.
When you get stuck like this, try thinking of a similar situation you do know the answer to.

Hint: you know ice floats approximately 90% submerged? (nine-tenths)

What is the density of ice divided by the density of liquid water?
What is that as a percentage?
 
Okay that makes sense. In this same question, it asks to draw a free body diagram to find all the forces. I only found the buoyant force and the gravity force and those don't allow me to have two densities. So did I do the FBD wrong and I'm missing some forces or do I rearrange archimedes' principle to substitute another density? Hope this makes sense.
 
Is the buoyant force related to the densities?
 
I'm assuming so that way I can solve for the percentage.
 
So if you have a buoyant force in your free body diagram, that accounts for the two densities right?
 

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