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.

• A. 1:3
• B.
• C.
• D. none of these

Answer 1

The correct option is B

Number of cubes = $\frac{2a\times 3a\times 9a}{3\times 3\times 3}$ = 2a${}^3$
Diagonal of a cube = $\sqrt{4a^2+9a^2+81a^2}$
Sum of the diagonals of cubes = 2a${}^3$ $\times$ 3$\sqrt{3}$
Ratio = $\frac{\sqrt{4a^2+9a^2+81a^2}}{2a^3\times 3\sqrt{3}}$