Question

the radius of Jupiter is 11 times the radius of earth calculate the ratio of the volume of Jupiter and Earth how many earth can Jupiter accommodate

Answer 1

$v = 4 \div 3\pi \: {r}^{3} \\ (4 \div 3) \times 3.14 \times {(11r) }^{3}$
On solving we get;
1331 * 3.14 * r^3 * 4/3
4179 *4/3
5572 Earth planets can be accommodated

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.