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You could gain an approximation by treating it as occupying a cuboid of length = (total length - the radiiof the approximately hemicylindrical ends) and of width and thickness the averages of the boards' actual dimensions; then adding the two semicircular volumes. The ends' radii may differ. Then add the volume of the fin, which should be a lot easier to calculate.

To obtain an accurate measurement you have 2 options.

1) Divide its mass by the density of its material (if you canfind that).

2) Use displacement in water - measure the volume of the water displaced by the board's total submersion in it, then use the relationship 1cubic metre = 1000 litres. (Or the corresponding cubic feet / gallon ratio.)

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