Question

Please explain how to do

Answer 1

$\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ a)\\\\ \cfrac{large~vase}{small~vase}\qquad 3:2\qquad \cfrac{3}{2}\qquad \cfrac{3^3}{2^3}=\cfrac{1080}{x}\implies x=\cfrac{2^3\cdot 1080}{3^3} \\\\\\ x=320 \\\\\\ b)\\\\ \cfrac{large~vase}{small~vase}\qquad 3:2\qquad \cfrac{3}{2}\qquad \cfrac{3^2}{2^2}=\cfrac{x}{252}\implies \cfrac{3^2\cdot 252}{2^2}=x \\\\\\ 567=x$