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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 accommodate?

Solution:

Assume Earth and Jupiter to be perfect spheres.
Let radius of Earth be Re = R (i)
Radius of Jupiter RJ = 11R. (ii)
Volume of earth Ve = (4/3)πR³ (iii)
Volume of Jupiter VJ = (4/3)πRJ³
VJ = (4/3)π(11R)³ = (4/3)πR³ × 1331. (iv)
Dividing (iv) by (iii),
VJ/Ve = [(4/3)πR³ × 1331] / [(4/3)πR³] = 1331
Hence, Jupiter can accommodate 1331 earths.