Pyrethrin is an insecticide derived from the pyrethrum plant. Polymeric supports are impregnated with pyrethrin and the insecticide slowly diffuses through the polymer and into a room (for example, Shell's No-Pest Strip \({ }^{\mathrm{TM}}\) ). The lethal concentration for most insects is about \(5 \times 10^{-4} \mathrm{mg} / \mathrm{m}^{3}\). A spherical pyrethrin delivery device is suspended from the ceiling of a room. The concentration of pyrethrin in the polymer is \(1 \mathrm{wt} \%\) and may be assumed constant over time. The density of the delivery device is \(0.96 \mathrm{~g} / \mathrm{cm}^{3}\) and its radius is \(6 \mathrm{~mm}\). The diffusivity of pyrethrin in air is \(0.03 \mathrm{~cm}^{2} / \mathrm{s}\) and its molecular weight is \(328 \mathrm{~g} / \mathrm{mol}\). How long will it take for the lethal concentration to be reached at a point \(3 \mathrm{~m}\) from the delivery device? Assume no interfacial resistance in getting the pyrethrin from the polymer and into the air.