Mathematics, 21.12.2019 08:31 vick67
The volumes of two similar figures 27mm^3 and 1331mm^3. if the surface area of the smaller figure is 18mm^2, what is the surface area of the larger figure
Answers: 1
![\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}}\\\\ -------------------------------\\\\](/tpl/images/0428/8767/70089.png)
![\bf \cfrac{small}{large}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\qquad thus\qquad \cfrac{\sqrt[3]{27}}{\sqrt[3]{1331}}=\cfrac{\sqrt{18}}{\sqrt{a}} \\\\\\ \cfrac{3}{11}=\sqrt{\cfrac{18}{a}}\implies \left( \cfrac{3}{11} \right)^2=\cfrac{18}{a}\implies \cfrac{3^2}{11^2}=\cfrac{18}{a}\implies a=\cfrac{11^2\cdot 18}{3^2}](/tpl/images/0428/8767/96b05.png)
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The volumes of two similar figures 27mm^3 and 1331mm^3. if the surface area of the smaller figure is...
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