Three solid cubes have a face diagonal of `4sqrt(2)` cm each. Three other solid cubes have a face diagonal of `8sqrt(2)` cm each. All the cubes are melted together to form a cube. Find the side of the cube formed in cm).

Options

A. `root(3)(324)`
B. `root(3)(576)`
C. 12
D. 24

Answer

C

Explanation

Side of each of the first three cubes `=(4sqrt(2))/(sqrt(2))=4 cm.`
Side of each of the other three cubes `=(8sqrt(2))/(sqrt(2))`
`=8 cm`.
Let the side of the cube formed be a cm.
Total volume of the six cubes `=3(4^(3)+8^(3))=3(64+512)=1728 cm^(3)`.
` :. a^(3) = 1728`
`a=12`.