Mass of a substance can be determined by its density and volume. The equation for mass (M) is density (D) divided by volume (V) or conversely D = MV. In this example the volume is 1 cubic meter (1m^3). Paper density is dependent on its type. Once density is known the weight of one cubic meter can be determined.
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It depends what the waste is and how densely it is packed. Imagine a cubic meter of un-crushed aluminum cans, and a cubic meter of crushed aluminum cans; Now imagine a cubic meter of newspaper, they would all weigh different amounts.