Respuesta :
[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \cfrac{s^2}{s^2}=\cfrac{81}{361}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{81}{361}\implies \cfrac{s}{s}=\sqrt{\cfrac{81}{361}} \\\\\\ \cfrac{s}{s}=\cfrac{\sqrt{81}}{\sqrt{361}}\implies \cfrac{s}{s}=\cfrac{9}{19}\impliedby \textit{scale factor of small:large}[/tex]
[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \cfrac{s^2}{s^2}=\cfrac{81}{361}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{81}{361}\implies \cfrac{s}{s}=\sqrt{\cfrac{81}{361}} \\\\\\ \cfrac{s}{s}=\cfrac{\sqrt{81}}{\sqrt{361}}\implies \cfrac{s}{s}=\cfrac{9}{19}\impliedby \textit{scale factor of small:large}[/tex]
The scale factor of a prism with the surface area of 81 m² to a similar prism with the surface area of 361 m² is 9 / 19.
What is scale factor?
Scale factor is the ratio of the corresponding sides of two similar figures.
If the scale factor of two similar figures is a/b, then the ratio of their areas is a² / b².
Therefore, the scale factor of a prism with the surface area of 81 m² to a similar prism with the surface area of 361 m² is as follows:
scale factor = √81 / √361
scale factor = 9 / 19
learn more on scale factor here:https://brainly.com/question/14967117
