Question

The radius of jupiter is 11 times the radius of the earth . Calculate the ration of the volumes of jupiter and earth . How many earth can jupiter accomodate ?

Answer 1

Let the radius of earth be r, then radius of Jupitor be 11r.
As the Jupitor and earth is a sphere, hence the volume of sphere is given by $\frac{4}{3}{\mathrm{\pi r}}^3$
So volume of jupitor = $\frac{4}{3}\mathrm{\pi }\times (11\mathrm{r}{)}^3$
And volume of earth = $\frac{4}{3}{\mathrm{\pi r}}^3$
So ratio of volume of jupitor : earth = $\frac{{\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^3(11{)}^3}{{\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^3}={11}^3$
So 11³ earth can be accommodated in the Jupitor.