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Because work is equal to -p delta V, to find the volume of the pump, you need to use the formula for calculating the volume of a cylinder which is pi (r)^2 X height, with the height being -20 because the pump is being compressed. Using the volume and the given pressure, you can plug the values into the equation to find the work.
Because the problem describes an irreversible expansion with a constant external pressure, you use the equation w=-P(ex)(deltaV). The delta V is equal to the area of the region compressed or expanded times the distance compressed. Therefore the diameter given is used to find the area of the region compressed and you plug in the rest of the given numbers.
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