Question

1.71 kg of glass (ρ = 2.66 x 10^3 kg/m3) is shaped into a hollow spherical shell that just barely floats in water. What are the (a) outer and (b) inner radii of the shell? Do not assume the shell is thin.

Volume = 2.66 * 10^3/1.71
V=1555.56 m^3
V=pi(r^2)h

Answer 1

Volume of Glass = (4/3) pi (Ro^3 - Ri^3)

mass of glass = rho V
so
1.71 = 2660 (4/3) pi (Ro^3-Ri^3)
so

(Ro^3 - Ri^3) = 4.8214*10^-4

Now Archimedes assume rho water = 1000
1000 (4/3)pi Ro^3 = 1.71

solve for Ro^3
go back and get Ri^3
take cube roots :)

Answer 2

By the way, your formula is for the volume of a cylinder, not a sphere. Use (4/3)pi r^3