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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 accommodate?

15. 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?

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Given that the radius of Jupiter is 11 times the radius of the earth.                                                         

So, let us assume that

the radius of Earth is 'r' then the radius of Jupiter will be '11r'.

So, as we know that the Volume of a sphere having radius 'x' is equal to  \frac{4}{3}\times \pi \times x^{3}

Then, the Volume of the earth would be

V_{earth} =  \frac{4}{3}\times \pi \times r^{3}

and Volume of Jupiter will be

V_{jupiter} =  \frac{4}{3}\times \pi \times (11r)^{3} 

               = (1,331)\times \frac{4}{3}\times \pi \times r^{3}.

So, the ratio of volumes is 

\frac{V_{jupiter}}{V_{earth}} = 1,331.

Hence we can conclude that 1,331 Earths can be accommodated in the planet Jupiter.

 

Posted by

Divya Prakash Singh

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