A spherical shell has an outside radius of 2.80 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.92 g/cm3. The space inside the shell is filled with a liquid having a density of 1.18 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a. m = g (b) For what value of a does m have its maximum possible value? a = cm (c) What is this maximum mass? m = g (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.