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 Earths can Jupiter accommodate?

Answer 1

Assume Earth and Jupiter to be perfect spheres.

Let radius of Earth be $R_e=R.....................\left(i\right)$

Radius of Jupiter $R_J=11R......................\left(ii\right)$

Volume of earth $V_e=\frac{4}{3}\pi R^3..............\left(iii\right)$

Volume of Jupiter $V_J=\frac{4}{3}\pi R_J^3$

$V_J=\frac{4}{3}\pi (11R{)}^3=\frac{4}{3}\pi R^3\times \mathrm{1331..............}(iv)$

Dividing $\left(iv\right)by\left(iii\right),$

$\frac{V_J}{V_e}=\frac{\frac{4}{3}\pi R^3\times 1331}{\frac{4}{3}\pi R^3}$

$=1331$

Hence, Jupiter can accommodate 1331 earths.