Question

if the radius of a sphere is doubled, then find the ratio of volume of first sphere to that of 2nd sphere ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{original}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere}=\mathrm{r} \\ \mathrm{Now},\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{original}\mathrm{sphere},{\mathrm{V}}_1=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \mathrm{Now},\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}=\mathrm{R}=2\mathrm{r} \\ \mathrm{Volume}\mathrm{of}\mathrm{new}\mathrm{sphere},{\mathrm{V}}_2=\frac{4}{3}{\mathrm{\pi R}}^3=\frac{4}{3}\mathrm{\pi }{\left(2\mathrm{r}\right)}^3=\frac{32{\mathrm{\pi r}}^3}{3} \\ \mathrm{Now},\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=\frac{4{\mathrm{\pi r}}^3}{3}÷\frac{32{\mathrm{\pi r}}^3}{3}=\frac{4}{3}\times \frac{3}{32}=\frac{1}{8} \end{gathered}$$