Question

The radius of jupiter is 11 times the radius of the earth. Calculate the ratio of the volumes of jupiter and the earth. Hau many earths can jupiter accommodate?

Answer 1

$\huge \bf \green{solution:-}$

$\sf\bold{{The \: radius \: of \: the \: earth \: is \: r. }} \\ \sf \bold{ {And \: the \: radius \: of \: the \: Jupiter \: is \: 11r.}} \\ \sf \bold{ {\: Ratio \: of \: the \: volumes \: of \: Jupiter \: and \: earth \: is}}$

$\sf \bold{ = \frac{ \frac{4}{3}\pi(11r) {}^{3} }{ \frac{4}{3\pi r {}^{3} } } = \frac{(11) {}^{3} }{1} = 1331 \ratio1 \: or \: \frac{1331}{1} }$

$\sf\bold{{1331 \: earth \: can \: be \: accommodated \: within \: jupiter.}}$

Answer 2

Therefore, the ratio of the volumes of Jupiter and the Earth are 1:1331 . Therefore 1331 Earths can be accommodated in Jupiter. Hence, option (A) is correct. The correct formula for volume of sphere of radius R is 43ΠR3 .