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1. If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes will be ?

A. 1 : 3

B. 2 : 3

C. 5 : 9

D. 7 : 9

Solution:

Let the length of each edge of each cube be a
Then, the cuboid formed by placing 3 cubes adjacently has the dimensions 3a , a and a
Surface area of the cuboid :

\begin{aligned} = 2 [3 a \times a + a \times a + 3 a \times a] \\ = 2 [3 a^{2} + a^{2} + 3 a^{2}] \\ = 14 a^{2} \end{aligned}

Sum of surface area of 3 cubes :

\begin{aligned} = (3 \times 6 a^{2}) \\ = 18 a^{2} \end{aligned}

∴ Required ratio :

\begin{aligned} = 14 a^{2} : 18 a^{2} \\ = 7 : 9 \end{aligned}

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