With no wastage, small cubes of side 3 inches are formed from a cuboid with the

Question

With no wastage, small cubes of side 3 inches are formed from a cuboid with the dimensions 2:3:9 are formed. Find the ratio of the body diagonal of the cuboid to that of all of the cubes.

Options:

A . 1:3

B . Ratio = √946a23√3

C . Ratio = √65a23

D . none of these

Answer: Option B
:
B
Number of cubes =

\frac{2 a \times 3 a \times 9 a}{3 \times 3 \times 3}

= 2a

^{3}

Diagonal of a cube =

\sqrt{4 a^{2} + 9 a^{2} + 81 a^{2}}

Sum of the diagonals of cubes = 2a

^{3}

\times

\sqrt{3}

Ratio =

\frac{\sqrt{4 a^{2} + 9 a^{2} + 81 a^{2}}}{2 a^{3} \times 3 \sqrt{3}}

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