Question

The volume of two spheres are in the ratio 64:27. Find the ratio of their radii.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{given}\mathrm{spheres}\mathrm{be}\mathrm{R}\mathrm{and}\mathrm{r}\mathrm{respectively}. \\ \mathrm{Given}:\mathrm{Ratio}\mathrm{of}\mathrm{volumes}=64:27 \\ \Rightarrow \frac{{\displaystyle \frac{4}{3}}{\mathrm{\pi R}}^3}{\frac{4}{3}{\mathrm{\pi r}}^3}=\frac{64}{27} \\ \Rightarrow \frac{{\displaystyle {\mathrm{R}}^3}}{{\mathrm{r}}^3}=\frac{64}{27} \\ \Rightarrow \frac{{\displaystyle \mathrm{R}}}{\mathrm{r}}=\frac{4}{3} \\ \mathrm{Thus},\mathrm{ratio}\mathrm{of}\mathrm{their}\mathrm{radii}\mathrm{is}4:3 \end{gathered}$$