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Question 15

A box of dimension $$40\times35\times28\text{ units}$$ is used to keep smaller cuboidal boxes so that no space is left between the boxes. If the box is packed with $$100$$ such smaller boxes of the same size, then dimension of the smaller box is

The large box has volume $$40\times35\times28=39200$$ cubic units. Dividing by $$100$$ gives $$392$$ cubic units per small box, and $$392=7\times8\times7$$. Therefore the small box has dimensions $$7\times8\times7$$ units.

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