Mathematics, 07.07.2019 18:50 roseemariehunter12
The height of one square pyramid is 12 m. a similar pyramid has a height of 6 m. the volume of the larger pyramid is 400 m3. determine each of the following, showing all your work and reasoning. scale factor of the smaller pyramid to the larger pyramid in simplest form ratio of the areas of the bases of the smaller pyramid to the larger pyramid ratio of the volume of the smaller pyramid to the larger volume of the smaller pyramid
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/0062/7329/e3ab0.png)
![\bf \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt[3]{volume}}{\sqrt[3]{volume}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{volume}{volume}} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{volume}{volume} \implies \cfrac{1^3}{2^3}=\cfrac{volume}{volume}\implies \cfrac{1}{8}=\cfrac{volume}{volume}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{1}{8}=\cfrac{\stackrel{volume}{v}}{\stackrel{volume}{400}}\implies \cfrac{1\cdot 400}{8}=v](/tpl/images/0062/7329/48bf7.png)
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