Question

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Answer 1

Given edge of three solid cubes are 3 cm , 4 cm and 5 cm respectively
Volume of cube $=(side{)}^3$
Volume of first cube $=(3{)}^3=27c{m}^3$
Volume of second cube $=(4{)}^3=64c{m}^3$
And Volume of third cube $=(5{)}^3=125c{m}^3$
$\therefore$ Sum of volume of three cubes $=(27+64+125)=216c{m}^3$
Let the edge of the resulting cube = R cm
Then, Volume of the resulting cube
$R^3=216c{m}^3$
$\therefore R=\sqrt[3]{3216c{m}^3}$
$\Rightarrow R=6cm$