Question

The radius of Jupiter is 11 times the radius of the earth. Calculate the ratio of the volumes of Jupiter and the earth.
How many earth can Jupiter accommodate?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{Jupitor}\mathrm{be}{r}^{\mathit{,}}. \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ {r}^{\mathit{,}}=11r \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{material}\mathrm{with}\mathrm{radius}r=\frac{4}{3}\pi r^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{Earth},\mathrm{V}=\frac{4}{3}\pi r^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{Jupitor},{\mathrm{V}}^{,}=\frac{4}{3}{{\mathrm{\pi r}}^{,}}^3 \\ {\mathrm{V}}^{,}=\frac{4}{3}\mathrm{\pi }(11\mathrm{r}{)}^3 \\ \mathrm{Ratio}\mathrm{of}\mathrm{volumes}=\frac{\frac{4}{3}\mathrm{\pi }(11\mathrm{r}{)}^3}{\frac{4}{3}{\mathrm{\pi r}}^3}=1331:1 \end{gathered}$$

Thus, Jupitor can accommodate 1331 Earths in it.