Question

A metal of edge $12cm$ is melted and formed into the smaller cubes. If the edge of the two smaller cubes are $6cm$ $8cm$, find the edge of the third smaller cube.

Answer 1

Volume of large cube$=V_1+V_2+V_3$

Let the edge of the third cube be $x$cm

${123}^3=6^3+8^3+x^3$

$\Rightarrow 1728=216+512+x^3$

$\Rightarrow x^3=1728-728=1000$

$\Rightarrow x=10$cm

$\therefore$ Length of third side$=10$cm