A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, the edge of the third smaller cube is?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 cm
When the metal is melted and recast, its volume does not change, so the volumes of the three small cubes add up to the volume of the big cube (volume of a cube of edge \(a\) is \(a^{3}\)).
Volume of the big cube: \(12^{3}=1728\,\mathrm{cm^3}\)
Volumes of the two known cubes: \(6^{3}+8^{3}=216+512=728\,\mathrm{cm^3}\)
Volume of the third cube: \(1728-728=1000\,\mathrm{cm^3}\)
Its edge: \(\sqrt[3]{1000}=\) 10 cm