Question

Three cubes of metal whose edges are in the ratio $3:4:5$ are melted down into a single cube whose diagonal is $12\sqrt{3}$ cm Find the edge of smallest of the three given cubes

• A. $6$ cm
• B. $2$ cm
• C. $4$ cm
• D. $1$ cm

Answer 1

The correct option is A $6$ cm

Diagonal of the new cube $=\sqrt{3}\times edge$
$=12\sqrt{3}\left(given\right)$
$\therefore$ edge of the new cube $=12cm$
Thus its volume $={12}^3=1728c{m}^3$
Let edge of the three cubes be $3x,4x,5x,$ respectively
${\left(3x\right)}^3+{\left(4x\right)}^3+{\left(5x\right)}^3=1728$
or $216x^3=1728$
$\therefore x^3=1728÷216=8$
$x=2$
$\therefore$ Edge of the smaller cube $=3x=3\times 2=6cm$