The density of a liquid is to be determined by an old $1$ $cm$ diameter cylindrical hydrometer whose division marks are completely wiped out. The hydrometer is first dropped in water of density $1000$ $kg/m^3$, and the water level is marked. The hydrometer is then dropped into the other liquid, and it is observed that the mark for water has risen $0.25$ $cm$ above the liquid-air interface. If the height of the watermark is $16$ $cm$, determine the density of the liquid. Note: Treat the hydrometer as being perfectly cylindrical. $\rho_{liquid}=$ $kg/m^3$