Q.15 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?

Let us consider Jupiter and Earth are two spheres with radii R and R' respectively.
Given in the question is that the radius of Jupiter is 11 times the radius of the Earth.

Radius of Earth = 11 x Radius of Jupiter
This implies, R’= 11 x R

As we know that volume of sphere of radius r is given as = (4/3) x (22/7) x r³

Volume of Earth = (4/3) x (22/7) x (R')³ = (4/3) x (22/7) x (11 x R )³

Volume of Jupiter = (4/3) x (22/7) x (R)³

The ratio of the volume of Jupiter to the volume of Earth is as follows:

Volume of Jupiter / Volume of Earth

= (4/3) x (22/7) x (R)³ / (4/3) x (22/7) x (11 x R )³

= 1 / 1331

Therefore, this ratio suggests that Jupiter can accommodate 1331 numbers of Earth in it.