Q. A spherical shell has an outside radius of 2.6cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.70g/ cm3. The space inside the shell is filled with a liquid having a density of 1.23g/cm3.

(1) Find the mass m of the sphere, including its contents, as a function of a. 
(2) In the answer to part (a), if a is regarded as a variable, for what value of a does m have its 
maximum possible value? 
(3) What is this maximum mass? 
(4) Does the value from part (b) agree with the result of a direct calculation of the mass of a sphere of uniform density? 
(5) For what value of a does answer to part (a) have its minimum possible value? 
(6) What is this minimum mass? 
(7) Does the value from part (f) agree with result of a direct calculation of the mass of a uniform sphere? 
(8) What value of m is halfway between the utmost and least amount possible values? 
(9) Does this mass agree with the result of part (a) evaluated for a = 2.60 cm/2 = 1.30 cm? 
(10) Explain whether you must expect agreement in each of parts (d), (g), and (i). 
(11) What If? In part (a), would answer change if the inner wall of the shell were not concentric with the outer wall?