A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is $\_\_\_\_$ $\pi \times 10^{-13} \mathrm{~m}^{3} / \mathrm{s}$.