Question

Three metallic solid cubes whose edges are$3cm,4cmand5cm$ are melted and formed into a single cube. Find the edge of the cube so formed.

Answer 1

Given

Side of first cube,$a_1=3cm$

Side of second cube, $a_2=4cm$

Side of third cube, $a_3=5cm$

These $3$ cubes are melted to form a single cube
Let us assume that the side of cube recast from melting these cubes is$S$

We know that the total volume of the $3$ cubes will be the same as the volume of the newly formed cube,

$Volumeofnewcube=(volumeof1st+2nd+3rdcube)$

We know that,

$Volumeofcube=a3,$

where $a=sideofcube$

$Volumeofnewcube=(volumeof1st+2nd+3rdcube)$

$\Rightarrow S^3={a^3}_1+{a^3}_2+{a^3}_3$

$\Rightarrow S^3={\left(3\right)}^3+{\left(4\right)}^3+{\left(5\right)}^3$

$\Rightarrow S^3=27+64+125=216$

$\Rightarrow S=6cm$
Therefore, side of cube so formed is $6$ cm.