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1. 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

Solution:

\begin{aligned} Volume of the large cube \\ = (3^{3} + 4^{3} + 5^{3}) = 216 c m^{3} \\ Let the edge of the large cube be a \\ S o, a^{3} = 216 \Rightarrow a = 6 c m \\ ∴ Required ratio \\ = \frac{6 \times (3^{2} + 4^{2} + 5^{2})}{6 \times 6^{2}} \\ = \frac{50}{36} \\ = 25 : 18 \end{aligned}

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