Question

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is:

Answer 1

The edges of three cubes are 6 cm, 8 cm and 10 cm, respectively.
$\therefore$ Sum of volumes of the three metal cubes
$=6^3+8^3+{10}^3$ $[\because volumeofcube=(edge{)}^3]$
$=216+512+1,000$
$=1,728c{m}^3$

Since a new cube is formed by melting these three cubes, the volume of the new cube formed is equal to the sum of the volume of the other cubes.
Let $a$ be the side of new cube.
So, the volume of the cube formed = $a^3$
Now, $a^3=1,728c{m}^3$
$\Rightarrow a=12cm$
Hence, the edge of the new cube formed is 12 cm.