Weight of Sugar

   Can you tell what is heavier – a cup of lump sugar or a cup of powdered sugar?

Answer:   The problem may seem tricky, but it is actually very simple.

                Let the diameter of lump sugar be 100 times of powdered sugar. And let us assume that the diameter of the sugar particles and the cup which they fill increase 100 times. Then the capacities of the cup will increase 100 X 100 X 100 = 1000000 times proportionally.

                 Next, let us measure out an ordinary cup of such enlarged powered sugar i.e. one millionth part of the contents of our giant cup. It will, of course, weigh exactly the same as an ordinary glass of ordinary powdered sugar.

                Then the question arises, what does our enlarged powered sugar represent? Just a lump of sugar.

                 Lump sugar is geometrically similar to powdered sugar and it makes no difference if we enlarge a sugar particle 60 times instead of 100. A cup of lump sugar weights the same as a cup of powdered sugar.