Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If three cubes of copper, each with an edge of 6 cm 8 cm and 10 cm respectively are melted to form a single cube, then the diagonal of the new cube will be
(a)18 cm
(b)19 cm
(c)19.5 cm
(d)20.8 cm
Answer
Answer (as printed): D
Explanation
Volume of the new cube $=\left(6^{3}+8^{3}+10^{3}\right) \mathrm{cm}^{3}=1728 \mathrm{cm}^{3}$. Let the edge of the new cube be $a$ cm. $$\therefore a^{3}=1728 \Rightarrow a=12 .$$ Hence, length of diagonal $=\sqrt{3} a=12 \sqrt{3} \mathrm{cm}$ $$=(12 \times 1.732) \mathrm{cm}=20.784 \mathrm{cm} \approx 20.8 \mathrm{cm} \text {. }$$