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?

AcademicPhysicsNCERTClass 8

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.
raja
Updated on 10-Oct-2022 13:25:32

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