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A spherical shell has an outside radius of 2.45 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.74 g/cm3. The space inside the shell is filled with a liquid having a density of 1.19 g/cm3.

(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?

(d) Explain whether the value from part (c) agrees with the result of a direct calculation of the mass of a solid sphere of uniform density made of the same material as the shell.

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