Question

If the ratio of the volumes of 2 spheres is 8:27, what is the ratio of their radii?

Answer 1

`\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{cccllll} &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}\\\\ -----------------------------\\\\ volumes\to \cfrac{s^3}{s^3}\textit{ ratio of sides is then }\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s} \\\\\\ volumes\to \cfrac{8}{27}\textit{ ratio of sides is then }\cfrac{\sqrt[3]{8}}{\sqrt[3]{27}}`

and surely, you know how much is that