Question

What is the similarity ratio of the smaller to the larger similar cylinders?

Answer 1

4:5

Explanation:

Answer 2

`\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{√(s^2)}{√(s^2)}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\`


`\bf \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{√(48\pi )}{√(75\pi )}\implies \cfrac{s}{s}=\cfrac{√((2^2)^2\cdot 3)}{√(5^2\cdot 3)}\implies \cfrac{s}{s}=\cfrac{4√(3)}{5√(3)} \\\\\\ \cfrac{s}{s}=\cfrac{4}{5}`