Marbles are shipped in a cubic packing crate with a height of 2m. The marbles are solid glass spheres of 1cm diameter. Originally, the marbles are carefully packed in a simple cubic arrangement. In shipping, the marbles settle to the densest cubic packing arrangement. a) How many marbles are shipped in the crate? b)When the packing crate is opened at its destination, how far down from the top of the crate is the top layer of marbles?

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Marbles are shipped in a cubic packing crate with a height of 2m. The marbles are solid
glass spheres of 1cm diameter. Originally, the marbles are carefully packed in a simple
cubic arrangement. In shipping, the marbles settle to the densest cubic packing
arrangement.

a) How many marbles are shipped in the crate?

b)When the packing crate is opened at its destination, how far down from the
top of the crate is the top layer of marbles?

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