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Answer :
Given :
Side (a) of cube = 12 cm
We know that,
Volume of 8 cubes
= \({a}^3\)
= \({12}^3\) \({cm}^3\)
= 1728 \({cm}^3\).
Now, Let the side of the smaller cube be \(\left(a_{1}\right)\).
Thus, volume of 1 smaller cube
= \(\frac{1728}{8}\) \({cm}^3\)
\(\Rightarrow \) \({\left(a_{1}\right)}^3\) = 216 \({cm}^3\)
\(\Rightarrow \) \(\left(a_{1}\right)= 6 cm \)
Therefore, the side of the smaller cubes will be 6 cm.
Ratio between surface areas of cube
= \(\frac{Surface area of bigger cube}{Surface area of smaller cube}\)
= \([\frac{6 × \left(a_{2}\right)^2}{6 × \left(a_{1}\right)^2}]\)
= \((\frac{12}{6})^2\)
= \((\frac{2}{1})^2\)
= \(\frac{4}{1}\)
Therefore, the ratio between the surface areas of these cubes is 4:1.