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Is the buoyancy force independent of the location of the object in the fluid?

From what I got out of Archimedes principle, it essentially states that the buoyancy force is the weight of the fluid in which the object is submerged in. But in my general physics class, it states that the buoyancy force equals the density of the fluid times gravity times the volume in which the object displaces? So therefore, the force is dependent on the location of the of the object with respect to the fluid.

Please help me where I'm going wrong. I'm a beginner student.