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Two students are given cubic boxes, measuring 10 cm on a side. Robert puts a single glass marble with a diameter of 10 cm in the box. Susan puts 1,000 1-cm glass marbles in her box.

1.Whose box has more empty space? Explain.

2.Whose box will be heavier? Explain.

Can you help me figure this out? thank you!!

  • earth - ,

    since v = 4/3 pi r^3, when you replace r with 10r, you get

    4/3 pi (10r)^3 = 4/3 pi 1000 r^3 = 1000v

    so, one 10-cm ball has the same volume as 1000 1-cm balls.

    both boxes have the same empty space, and will weigh the same (since they have the same amount of glass inside).

  • earth - ,

    Since 1000 1-cm diameter marbles have the same volume as one 10 cm marble, the amount of free space would be the same.

    If the volumes of glass are the same, and the density of glass stays the same, the masses of both filled boxes would also be the same.

    The smaller marbles would try to form a hexagonal close packed array which would allow them to be stacked closer together. There would be open empty space at the top of the box of small marbles, but it would not affect the answer.

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