A sphere made of a hydrogel, has a radius of $100$ microns. It contains a drug at $0\mathrm{.}5$ mg$/$ml$.$ As the sphere is placed in a reservoir, the drug diffuses out of the sphere. Assume the reservoir is large enough that the drug concentration can be considered as zero. The drug diffusion coefficient is $5$ x$10^2$ um$^2/$s$.$Determine the time required for the drug concentration at the center of the sphere to equal $5\%$ of the initial concentration in the sphere.