You want to make spherical ice cube from a sugar solution to use in your cold coffee. The sugar syrup was made by adding $45g$ of a sugar $($of molecular weight $90)$ in $180g$ of water. Determine the time taken by the resulting solution $($density $=1,100k\frac{g}{m^3},$ thermal conductivity $=0\mathrm{.}7\frac{W}{m}-K)$ to freeze when placed in a metallic spherical mold $(4cm$ in diameter$)$ and the cylinder is surrounded by freezing medium at $-18C.$ Assume that the convective heat transfer coefficient between the solution and the freezing medium is $150\frac{W}{m^2}-K.$