Question

the radius of Jupiter is 11 times the radius of the Earth. Calculate the ratio of the volume of Jupiter and the Earth. How many Earths can Jupiter accommodate?​

Answer 1

Given:

• Radius of Jupiter = 11 times the radius of Earth.

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To find:

• Ratio of the volumes of Jupiter and Earth.
• Number of Earths that can accommodate in Jupiter.

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Solution:

If radius of Earth is taken as 1 unit, then the radius of Jupiter will be 11 units (11 times the radius of Earth).

Formula for calculating volume of a sphere:

$\boxed {\sf {\red {\dfrac {4}{3} \times \pi \times r^{3}}}}$

Where,

r = radius

π = constant (3.14)

• Volume of Jupiter = $\sf \dfrac {4}{3} \times \pi \times r^{3}$

$\sf \dfrac {4}{3}\times \pi \times (11)^{3}$

$\sf \dfrac {4}{3}\times \pi \times 1331$

• Volume of Earth = $\sf \dfrac {4}{3} \times \pi \times r^{3}$

$\sf \dfrac {4}{3}\times \pi \times (1)^{3}$

$\sf \dfrac {4}{3}\times \pi \times 1$

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Ratio:

$\sf \dfrac{Volume \: of \: Jupiter}{Volume \: of \: Earth}$

$\sf \dfrac{4 \times \pi \times 1331 \times 3}{4 \times 3 \times \pi \times 1}$

$\sf \dfrac{1331}{1}$

= 1331 : 1

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Final answer:

• Ratio of volume of Jupiter to volume of Earth is 1331 : 1.
• 1331 Earths can accommodate in Jupiter.