Question:
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6cm and 8cm, find the edge of the third smaller cube.
Solution:
Volume of the large cube = v1 + v2 + v3
Let the edge of the third cube be 'x' cm
$12^{3}=6^{3}+8^{3}+a^{3}$ [Volume of cube $=$ side $^{3}$ ]
$1728=216+512+x^{3}$
$\Rightarrow x^{3}=1728-728=1000$
⇒ x = 10 cm
Therefore, Side of third side = 10 cm