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$($Force on curved surface$)$ A gate in the form of a partial cylindrical surface $($called a Tainter gate$)$ holds back water on top of a dam as shown in the figure below. The radius of the surface is $20ft,$ and its length is $36ft.$ The gate can pivot about point A$,$ and the pivot point is $10ft$ above the seat, C$.$ Determine the magnitude of the resultant water force on the gate.

$F_G=$

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