Final answer:
The maximum mass that can hang without sinking from a 60.0-cm-diameter styrofoam sphere in water is determined by calculating the volume of the sphere, followed by applying Archimedes' Principle to find the buoyant force, which equals the weight of the displaced water.
Step-by-step explanation:
The subject of the question revolves around the concept of buoyancy, which is a principle of Physics concerning the ability of an object to float in a fluid. The question asks to determine the maximum mass that a 60.0-cm-diameter styrofoam sphere can support without sinking in water. This can be solved by applying the Archimedes' Principle which states that the buoyant force on a submerged object is equal to the weight of the fluid it displaces. The sphere's volume must equal the volume of water displaced when it is just about to submerge, and thus the maximum mass can be found by calculating the sphere's volume and then multiplying by the density of water (1000 kg/m3) to find the maximum displaced water mass, which equates to the maximum supported mass.