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The radius of Jupiter is 11 times the radius of the Earth. Cal

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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?

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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?

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Text solutionVerified

Assume Earth and Jupiter to be perfect spheres.

Let radius of Earth be

R_{e} = R ..................... (i)

Radius of Jupiter

R_{J} = 11 R ...................... (ii)

Volume of earth

V_{e} = \frac{4}{3} π R^{3} .............. (iii)

Volume of Jupiter

V_{J} = \frac{4}{3} π R_{J}^{3}

V_{J} = \frac{4}{3} π (11 R)^{3} = \frac{4}{3} π R^{3} \times 1331.............. (i v)

Dividing

(i v) b y (iii),

\frac{V _{J}}{V _{e}} = \frac{\frac{4}{3} π R ^{3} \times 1331}{\frac{4}{3} π R ^{3}}

= 1331

Hence, Jupiter can accommodate 1331 earths.

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Question Text	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?
Answer Type	Text solution:1
Upvotes	151