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  4. A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a cm, and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid.

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Q. A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a $cm$, and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid.

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Solution:

$a^3: \sqrt{3} a \times \sqrt{2} a \times a=1: \sqrt{6}$