Given
Scale Factor of 2:7
When the scale factor is a:b
Recall the following
[tex]\begin{gathered} \text{The ratio of the sides is} \\ a:b \\ \; \\ \text{The ratio of the area is} \\ a^2:b^2 \\ \; \\ \text{The ratio of the volume is} \\ a^3:b^3 \end{gathered}[/tex]
Given that the ratio is is 2:7 then we have the following
[tex]\begin{gathered} \text{The ratio of the height of the model to the height of the original is} \\ 2:7 \\ \; \\ \text{The ratio of the surface area of the model to the surface area of the original is} \\ 2^2:7^2\Longrightarrow4:49 \\ \; \\ \text{The ratio of the volume of the model to the volume of the original is} \\ 2^3:7^3\Longrightarrow8:343 \end{gathered}[/tex]
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