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 6 cm and 8 cm, find the edge of the third smaller cube.

Answer 1

$\text{Edge of the metal cube}=12cm$

$\therefore \text{Its volume}=(Edge{)}^3=(12{)}^{3}c{m}^3$$=1728c{m}^3$

It is melted to form 3 smaller cubes.

$\text{Edge of one smaller cube}=6cm$

$\text{and edge of second smaller cube}=8cm$

$\therefore \text{Volume of two smaller cubes}=(6{)}^3+(8{)}^{3}c{m}^3$

$=216+512c{m}^3=728c{m}^3$

$\therefore \text{Volume of third smaller cube}=1728-728=1000c{m}^3$

$\therefore \text{Edge of the third cube}={1000}^{\frac{1}{3}}$$=10cm$