Question

Two pyramids are similar. The volume of the larger pyramid is 125 m³ and the volume of the smaller pyramid is 27 m³. The height of the smaller pyramid is 3 m.

What is the height of the larger pyramid?

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{√(s^2)}{√(s^2)}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{small}{large}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{3}{h}=\cfrac{\sqrt[3]{27}}{\sqrt[3]{125}}\implies \cfrac{3}{h}=\cfrac{3}{5}\implies \cfrac{3\cdot 5}{3}=h`

Answer 2

Answer: 5

Explanation:

I got it right on my test