$3\mathrm{.}68$ A spherical tank for storing liquid oxygen on the space shuttle is to be made from stainless steel of $0\mathrm{.}80-m$ outer diameter and $5-mm$ wall thickness. The boiling point and latent heat of vaporization of liquid oxygen are $90$ K and $213k\frac{J}{k}g,$ respectively. The tank is to be installed in a large compartment whose temperature is to be maintained at $240$ K $.$ Design a thermal insulation system that will maintain oxygen losses due to boiling below $1k\frac{g}{?}$ day.