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?

Explanation

Assume Earth and Jupiter to be perfect spheres.
Let radius of Earth be `"R"_(e) = "R "(i)`
Radius of Jupiter `"R"_(j) = 11"R "(ii)`
Volume of earth `V_(e) = (4)/(3) pi R^3 " "(iii)`
Volume of Jupiter `V_(j) = (4)/(3) pi R_(j)^(3)`
`V_(j) = (4)/(3) pi (11R)^(3) = (4)/(3) pi R^(3) xx 1331`
Dividing (iv) by (iii),
`(V_j)/( V_e) = ((4)/(3) pi R^3 xx 1331)/( (4)/(3) pi R^3)`
`=1331`
So, Jupiter can accommodate 1331 earths.