Ncert solutions

Question 15

Q 15) 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 accomodate?

Solution 15:

The volume of sphere = 4/3 ℼr3

Let the radius of the earth be ‘r’

The radius of Jupiter = 11 ✕ r

The volume of earth = 4/3 ℼr3

The volume of Jupiter = 4/3 ℼ (11r)3

= 4/3 ✕ (22 / 7) ✕ (11 ✕ r)3

Required\ ratio=\frac{Volume\ of\ the\ Jupiter}{Volume\ of\ the\ Earth}=\frac{\frac{4}{3}\times\left(\frac{22}{7}\right)\times1331\times r^3}{\frac{4}{3}\times\left(\frac{22}{7}\right)\times r^3}=1331

i.e. 1331 : 1

The volume of Jupiter is 1331 times the volume of the earth. Thus, around 1331 earths can fit into one jupiter.

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