Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2005 · Marks: · Difficulty:
A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is
(a)2 : 1
(b)3 : 2
(c)25 : 18
(d)27 : 20
Answer
Answer (as printed): C
Explanation
Volume of the larger cube $=\left(3^{3}+4^{3}+5^{3}\right) \mathrm{cm}^{3}=216 \mathrm{cm}^{3}$. Let the edge of the larger cube be $a$ cm. $$\therefore a^{3}=216 \Rightarrow a=6 .$$ Required ratio $=\frac{6\left(3^{2}+4^{2}+5^{2}\right)}{6 \times 6^{2}}=\frac{6 \times 50}{6 \times 36}=\frac{25}{18}$.