Question

Three cubes with sides in the ratio 3:4:5 are melted to form a single cube whose diagonal is $12\sqrt{3}$cm, the sides of the cubes are:

• A. 3 cm, 4 cm, 5 cm
• B. 6 cm, 8 cm, 10 cm
• C. 9 cm, 12 cm, 15 cm
• D. 12 cm, 16 cm, 20 cm
• E. None of these

Answer 1

The correct option is B

6 cm, 8 cm, 10 cm

Let the sides of the three cubes be 3x, 4x, and 5x
Then, volume of the new cube = [(3x)${}^3$ + (4x)${}^3$ + (5x)${}^3$] = 216x${}^3$
Edge of the new cube = ${\left(216x^3\right)}^{\frac{1}{3}}$
Diagonal of the new cube $=6\sqrt{3}x$
$\therefore$$6\sqrt{3}x=12\sqrt{3}\Rightarrow x=2$
So, the sides of the cubes are 6 cm, 8 cm and 10 cm.