Question

Three cubes of edges $6$ cm, $8$ cm and $10$ cm respectively are melted without any loss of metal into a single cube. Find the edge of the new cube.

Answer 1

Volume of the new cube of edge x cm$\left(say\right)=x^3$
which is same as $6^3+8^3+{10}^3$
$x^3=(6^3+8^3+{10}^3)c{m}^3$
$=(216+512+1000)c{m}^3$
$=1728c{m}^3$
$={\left(12\right)}^{3}c{m}^3$
$x=12cm$