With no wastage, small cubes of side 3 inches are formed from a cuboid with the dimensions 2:3:9. Find the ratio of the body diagonal of the cuboid to that sum of diagonal lengths of all cubes.
Number of Cubes = 2a×3a×9a3×3×3=2a3
Diagonal of Cuboid = √4a2+9a2+81a2
Sum of the diagonals of cube = 2a3 × 3√3
Ratio = √4a2+9a2+81a22a3×3√3=√946a2√3