Question

The radius of Jupiter is 11 times the radius of Earth. Calculate the ratio of the volumes of Jupiter and the Earth. How many Earths can Jupiter accommodate?
(A) 1331
(B) 1221
(C) 111
(D) None of these

Answer 1

Hint
Since the planets are in the shape of a sphere we calculate the volumes of planets by applying the formula for volume of a sphere. We know that the volume of a sphere of radius R is ${\displaystyle \frac{4}{3}}\mathrm{\Pi }{R}^3$ . So first we calculate the volumes of Jupiter and Earth and then take their ratios. The ratio gives us the number of Earth’s can be accommodated in Jupiter.

Complete step by step answer
Let the radius of the Earth be $R_E$ and volume be $V_E$
Let the radius of the Jupiter be $R_J$ and volume be $V_J$
Given, $R_J=11R_E$
So, ${\displaystyle \frac{V_E}{V_J}}={\displaystyle \frac{{\displaystyle \frac{4}{3}}\mathrm{\Pi }{\left(R_E\right)}^3}{{\displaystyle \frac{4}{3}}\mathrm{\Pi }{\left(R_J\right)}^3}}={\displaystyle \frac{{\left(R_E\right)}^3}{{\left(R_J\right)}^3}}$
 $\Rightarrow {\displaystyle \frac{V_E}{V_J}}={\displaystyle \frac{{\left(R_E\right)}^3}{{\left(11R_E\right)}^3}}$
 $\Rightarrow {\displaystyle \frac{V_E}{V_J}}={\displaystyle \frac{1}{{\left(11\right)}^3}}$
 $\Rightarrow V_E:V_J=1:1331$
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.

Note
The correct formula for volume of sphere of radius R is ${\displaystyle \frac{4}{3}}\mathrm{\Pi }{R}^3$ . Most of the students go wrong here. Jupiter is the fifth planet from the sun and the largest planet in the whole solar system. It has more gravity than Earth. Gravity of Jupiter $24.79m{s}^{-2}$ .