Question

spaghetti sauce comes in large and small cylindrical cans. the larger can has a radius and height that are both three times longer than the radius and height of the smaller can. if the volume of the smaller can is 35.28, what is the volume of the larger can?

Answer 1

check the picture below.


`\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{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\cfrac{\sqrt[3]{35.28}}{\sqrt[3]{v}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{35.28}{v}} \\\\\\ \left( \cfrac{1}{3} \right)^3=\cfrac{35.28}{v}\implies \cfrac{1^3}{3^3}=\cfrac{35.28}{v}\implies v=\cfrac{3^3\cdot 35.28}{1^3}`