A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.
Given,
Edge of metal cube = 12 cm
Volume of cube = a3 = 123 = 1728 cm3
Edge of 2 smaller cube = 6cm , 8 cm
Let edge of 3rd cube = x cm
So, 63+83+ x3 = 1728
= x3 = 1728 – (216+512) = 1000
= x = 
13