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1. 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

Solution:

Volume of the larger cube :

\begin{aligned} = (3^{3} + 4^{3} + 5^{3}) c m^{3} \\ = 216 c m^{3} \end{aligned}

Let the edge of the larger cube be a cm

\begin{aligned} ∴ a^{3} = 216 \\ \Rightarrow a = 6 \end{aligned}

Required ratio :

\begin{aligned} = \frac{6 (3^{2} + 4^{2} + 5^{2})}{6 \times 6^{2}} \\ = \frac{6 \times 50}{6 \times 36} \\ = \frac{25}{18} O r 25 : 18 \end{aligned}

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