Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is $12 \sqrt{3} \mathrm{cm}$. 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)None of these
Answer
Answer (as printed): B
Explanation
Let the sides of the three cubes be $3 x, 4 x$ and $5 x$. Then, Volume of the new cube $=\left[(3 x)^{3}+(4 x)^{3}+(5 x)^{3}\right]$ $$=216 x^{3} .$$ Edge of the new cube $=\left(216 x^{3}\right)^{1 / 3}=6 x$. 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.
Explanation as extracted from the printed page; notation may be imperfect.