A solid carbon cylinder $($initial diameter of $3cm,$length of $20cm,$ and density of $0\mathrm{.}38\frac{g}{c}{m}^3)$ is suspended in still air. Oxygen diffuses from $4cm$

away from the center of this cylinder and reacts with carbon on the cylinder surface to produce only carbon dioxide which diffuses away from the carbon surface. The operating conditions are $1120K$ and $0\mathrm{.}976{10}^{5}Pa.$

the diffusion coefficient of oxygen in air is $0\mathrm{.}175\frac{c{m}^2}{s}.$ Determine the time required to reduce the diameter of this carbon to $0\mathrm{.}1cm.$