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 accomodate?

Answer 1

Let radius of earth = x km
So, radius of Jupiter = 11x km
Now,
Volume of earth =
$\frac{4}{3} \times \pi \times {x}^{3}$
Volume of Jupiter =
$\frac{4}{3} \times \pi \times {1331x}^{3}$
Ratio will be
Volume of earth / volume of jupiter.
This will result :
1/1331
So,
Ratio will be 1:1331.
Therefore,
Jupiter cam accomodate 1331 earths in it.

Hope this will be helping you....

Answer 2

Solution :

Let the radius of the Earth and Jupiter be "R"

Now ,
According to the Question :-

R = 11 R

So ,

$= > volume \: of \: the \: jupiter = \frac{4}{3} \pi \:(r)^{3}$

$= > \frac{4}{3} \pi(11r)^{3}$

Also ,

$= > volume \: of \: the \: earth = \frac{4}{3} \pi \: r^{3}$

Then ,

$= > \frac{volume \: of \: the \: jupiter}{volume \: of \: the \: earth}$

$= > \frac{ \frac{4}{3}\pi \:(11r)^{3} }{ \frac{4}{3}\pi \: r^{3} }$

$= > \frac{1331 \times \frac{4}{3} \pi \: r^{3} }{ \frac{4}{3} \pi \: r^{3} }$

$= > 1331$

Hence ,
Jupiter can accomodate 1331 Earths.