Question

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

• A. $\sqrt[3]{324}$
• B. $\sqrt[3]{576}$
• C. 12
• D. 24

Answer 1

Answer: (C)

Side of each of the first three cubes $=\frac{4\sqrt{2}}{\sqrt{2}}=4cm$.
Side of each of the other three cubes $=\frac{8\sqrt{2}}{\sqrt{2}}=8cm$.
Let the side of the cube formed be $acm$.
Total volume of the six cubes $=3\left(4^3+8^3\right)=3(64+512)=1728c{m}^3$
$\therefore a^3=1728$
$a=12$.