Answer:
The total charge of the shell is about 1.034 [tex]10^{-7}[/tex] Coulombs
Explanation:
In order to find the actual volume of the spherical shell ([tex]V_s[/tex]), we estimate the volume of the sphere with larger radius R, and subtract from it the volume of the sphere with smaller radius r:
[tex]V_s=\frac{4}{3} \pi\,R^3-\frac{4}{3} \pi\,r^3\\V_s=\frac{4}{3} \pi\,(R^3-r^3)\\V_s=\frac{4}{3} \pi\,(4.5^3-3.7^3)\,cm^3\\V_s=169.52871 \, cm^3\\V_s=0.00016952871 \, m^3[/tex]
Now, in order to find the shell's total charge, we multiply its volume times the volume charge density of the shell ([tex]6.1\,\,10^{-4}\,\frac{C}{m^3}[/tex]):
[tex]Total\,\,charge=0.00016952871\,m^3\,(6.1\,\,10^{-4}\,\frac{C}{m^3} = 1.034\,\,10^{-7}\,C[/tex]
