Problem

A hollow sphere of glass whose external and internal radii are 11 cm and 9 cm respectively is completely filled with ice at

0^\text{C}

and placed in a bath of boiling water. How long will it take for the ice to melt completely? Given that density of ice =

0.9 \text{ g/cm}^3

, latent heat of fusion of ice =

80 \text{ cal/g}

and thermal conductivity of glass =

0.002 \text{ cal/cm}\cdot\text{s}\cdot^\circ\text{C}