A gas is confined in a $1\mathrm{.}25(ft)$ diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is $370(lbm).$ The local acceleration of gravity is $32\mathrm{.}169(ft)(s{)}^{-2},$ and atmospheric pressure is $30\mathrm{.}12(inHg).$

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What is the force in $(($:$l{b}_f\}$ exerted on the gas by the atmosphere, the piston, and the weight, assuming no friction between the piston and cylinder?

The force exerted on the gas by the atmosphere, the piston, and the weight is Ibf.