[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------[/tex]
[tex]\bf \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}}\\\\
-------------------------------\\\\
a)\\\\
\cfrac{large~vase}{small~vase}\qquad 3:2\qquad \cfrac{3}{2}\qquad \cfrac{3^3}{2^3}=\cfrac{1080}{x}\implies x=\cfrac{2^3\cdot 1080}{3^3}
\\\\\\
x=320
\\\\\\
b)\\\\
\cfrac{large~vase}{small~vase}\qquad 3:2\qquad \cfrac{3}{2}\qquad \cfrac{3^2}{2^2}=\cfrac{x}{252}\implies \cfrac{3^2\cdot 252}{2^2}=x
\\\\\\
567=x[/tex]
