Question

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

• A. 2:1
• B. 3:2
• C. 25:18
• D. 27:20

Answer 1

The correct option is C

25:18

Volume of the large cube = (3${}^3$+4${}^3$+5${}^3$) cm${}^3$ = 216 cm${}^3$

Let the edge of the large cube be `a'

So, a${}^3$= 216 $\Rightarrow$ a = 6 cm

$\therefore$Required ratio = $\frac{6\times (3^2+4^2+5^2)}{6\times 6^2}=\frac{50}{36}=25:18$