Question

The volume of a cylinder is 10 cubic centimeters .  What is the volume of a cylinder with sides four times as large as the sides of the first cylinder?

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


`\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \cfrac{r}{4r}=\cfrac{h}{4h}=\cfrac{1}{4}\impliedby ratio \\\\\\ now\qquad \cfrac{1^3}{4^3}=\cfrac{\textit{smaller volume}}{\textit{larger volume}}\implies \cfrac{1}{64}=\cfrac{10}{v}\implies v=64\cdot 10`