$(20$ points$)$ In the figure, a spring of spring constant $3\mathrm{.}00{10}^4\frac{N}{m}$ is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area $A_i,$ and the output piston has area $18\mathrm{.}0A_i.$ Initially the spring is at its rest length. How many kilograms of sand must be $($slowly$)$ poured into the container to compress the spring by $5\mathrm{.}00$ cm $?$

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