Question

three cubes whose edges are 6,8 and 10cm respectively are melted without any loss of metal into a signal cube .find the edge of the new cube .

Answer 1

Let the edges of the three cubes be $a_{1}$ = 6 cm, $a_{1}$ = 8 cm, $a_{1}$ = 10 cm and the edge of the new single cube be A respectively.
It is given that the cubes are melted into a single cube without any loss in the metal.Therefore, the total volume of the three cubes is equal to the volume of the new large cube.
$(a_{1}) ^{3} +( a_{2})^{3} +( a_{3})^{3} = A^{3}$
$6^{3}+ 8^{3}+ 10^{3}= A^{3}$
[tex]216+512+1000= A^{3} [/tex]$1728= A^{3}  A^{3} = 12^{3}$
$A=12$
Therefore, the edge of the new cube is 12 cm in length.