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A spherical shell has an outside radius of 2.55 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.69 g/cm^3. The space inside the shell is filled with a liquid having a density of 1.09 g/cm^3.

(a) Find the mass m of the sphere, including its contents, as a function of a.

(b) For what value of a does m have its maximum possible value?

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