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In this particular type of question we need to proceed by expressing the sides of the cubes as a and b and finding the ratio between them. Then we need to use it in finding the ratio of surface area of both the cubes.

__Complete step-by-step answer:__

Let the sides of the cube be a and b.

Then,

We know that volume of a cube = ${side^3}$

Therefore ratio of the volumes = $\dfrac{{{a^3}}}{{{b^3}}}$

But ratio = $1:27$

$

\Rightarrow \dfrac{{{a^3}}}{{{b^3}}} = \dfrac{1}{{27}} \\

\Rightarrow {\left( {\dfrac{a}{b}} \right)^3} = {\left( {\dfrac{1}{3}} \right)^3} \\

\Rightarrow \dfrac{a}{b} = \dfrac{1}{3} \\

$

Therefore,

Ratio of the surface areas = $\dfrac{{6{a^2}}}{{6{b^2}}}$

(since surface area of the cube = $6 \times sid{e^2}$ )

$

= \dfrac{{{a^2}}}{{{b^2}}} \\

= {\left( {\dfrac{a}{b}} \right)^2} \\

= {\left( {\dfrac{1}{3}} \right)^2}{\text{ }}\left( {{\text{putting value of }}\dfrac{a}{b}{\text{ from above}}} \right) \\

= \dfrac{1}{9} \\

= 1:9 \\

$

Therefore ratio of the surface areas =$1:9$.

Note- Always recall the formula of volume and surface area of three dimensional figures like cube. Note that a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

In this particular type of question we need to proceed by expressing the sides of the cubes as a and b and finding the ratio between them. Then we need to use it in finding the ratio of surface area of both the cubes.

Let the sides of the cube be a and b.

Then,

We know that volume of a cube = ${side^3}$

Therefore ratio of the volumes = $\dfrac{{{a^3}}}{{{b^3}}}$

But ratio = $1:27$

$

\Rightarrow \dfrac{{{a^3}}}{{{b^3}}} = \dfrac{1}{{27}} \\

\Rightarrow {\left( {\dfrac{a}{b}} \right)^3} = {\left( {\dfrac{1}{3}} \right)^3} \\

\Rightarrow \dfrac{a}{b} = \dfrac{1}{3} \\

$

Therefore,

Ratio of the surface areas = $\dfrac{{6{a^2}}}{{6{b^2}}}$

(since surface area of the cube = $6 \times sid{e^2}$ )

$

= \dfrac{{{a^2}}}{{{b^2}}} \\

= {\left( {\dfrac{a}{b}} \right)^2} \\

= {\left( {\dfrac{1}{3}} \right)^2}{\text{ }}\left( {{\text{putting value of }}\dfrac{a}{b}{\text{ from above}}} \right) \\

= \dfrac{1}{9} \\

= 1:9 \\

$

Therefore ratio of the surface areas =$1:9$.

Note- Always recall the formula of volume and surface area of three dimensional figures like cube. Note that a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.