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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 accomodate?
Given:
The radius of Jupiter is 11 times the radius of the Earth.
To do:
We have to calculate the ratio of the volumes of Jupiter and the Earth. Also, we have to find out how many Earths can Jupiter accommodate.
Solution:
Let $r$ be the radius of the earth.
The radius of Jupiter $=11r$
The volume of sphere$=\frac{4}{3}\pi r^3$
The volume of earth, $V_{earth}=\frac{4}{3}\pi r^3$
The volume of Jupiter, $V_{jupiter}=\frac{4}{3}\pi (11r)^3$
$=1331(\frac{4}{3}\pi r^3)$
So, $\frac{Volume\ of\ the\ Jupiter}{volume\ of\ the\ earth}=\frac{V_{jupiter}}{V_{earth}}$
$=\frac{1331(\frac{4}{3}\pi r^3)}{\frac{4}{3}\pi r^3}$
$=\frac{1331}{1}$
Therefore, The volume of Jupiter is $1331$ times the volume of the earth. Thus, Jupiter can accommodate around $1331$ Earths.
Updated on: 10-Oct-2022
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