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

Earth and Jupiter can be considered as two spheres with radii R and R' respectively. Given that the radius of Jupiter is 11 times the radius of the Earth.
Thus, R' = 11 R
Volume of a sphere of the radius r is given as = $\frac{4}{3}\pi r^3$
Volume of the earth = $\frac{4}{3}\pi r^3$
And, volume of jupiter = $\frac{4}{3}\pi (R^{\prime }{)}^3=\frac{4}{3}\pi (11R{)}^3=1331(\frac{4}{3}-\pi R^3)$
The ratio of the volumes of jupiter and Earth
$=\frac{VolumeofJupiter}{VolumeofEarth}$
$=\frac{1331\left(\frac{4}{3}\pi R^3\right)}{\frac{4}{3}\pi r^3}=1331$
Hence, this ratio suggests that Jupiter can accomodate 1331 number of Earths within it.