Question

the edges of 3 solid cubes are 6 cm,8cm,10cm.these cubes qre melted and recasted into a single cube. find the edge of the resulting cube

Answer 1

edge of 1st cube=3cm
$volume = {side}^{3}$
$= {3}^{3}$
$= 27 {cm}^{3}$

edge of 2nd cube=4cm
$volume = {4}^{3}$
$64 {cm}^{3}$

edge of 3rd cube=5cm
$volume = {5}^{3}$
$= 125 {cm}^{3}$

$total \: volume \: of \: 3 \: cubes \\ = 27 {cm}^{3} + 64 {cm}^{3} + 125 {cm}^{3}$
$= 216 {cm}^{3}$

$volume = {side}^{3}$
$216 = {side}^{3}$
$side = \sqrt[3]{216}$
=6cm

edge of new cube is 6cm