Answer:
The answer is below
Explanation:
a) The volume of a sphere is:
Volume = (4/3)πr³; where r is the radius of the shell.
Given the outside radius of 2.60 cm and inner radius of a cm, the volume of the spherical shell is:
Volume of spherical shell = [tex]\frac{4}{3} \pi (2.6^3-a^3)[/tex] cm³
But Density = mass / volume; Mass = density * volume.
Therefore, mass of spherical shell = density * volume
mass of spherical shell = [tex]4.70\ g/cm^3[/tex] * [tex]\frac{4}{3} \pi (2.6^3-a^3)[/tex] cm³
Mass of liquid = volume of inner shell * density of liquid
Mass of liquid = [tex]\frac{4}{3} \pi a^3\ cm^3*1.23\ g/cm^3[/tex]
Total mass of sphere including contents = mass of spherical shell + mass of liquid
Total mass of sphere including contents (M) = [tex]4.70\ g/cm^3[/tex] * [tex]\frac{4}{3} \pi (2.6^3-a^3)\ cm^3[/tex] + [tex]\frac{4}{3} \pi a^3\ cm^3*1.23\ g/cm^3[/tex] =
Total mass of sphere including contents (M) = (346 - 14.5a³) grams
b) The mass is maximum when the value of a = 0
M = 346 - 14.5a³
M' = 43.5a² = 0
43.5a² = 0
a = 0
