The radius of Jupiter is 11 times the radius of the Earth .Calculate the ratio of the volumes of the Jupiter and the Earth. How many Earths can Jupiter accommodate?
Answers
Answer:
Let us consider Jupiter and Earth are two spheres with radii R and R’ respectively. Given in the question that radius of Jupiter is 11 times the radius of the Earth.
So, R’= 11R
Volume of sphere of radius r is given as = 4⁄3πr3
Volume of Earth = 4⁄3πr3
And, volume of Jupiter = π(R1)3
=4⁄3 π(R1)3=1331[4/3πR3]
The ratio of the volume of Jupiter and earth
=volume of Jupiter volume of Earth =1331(4/3πR3)4/3πR3=1331
Therefore, this ratio suggests that Jupiter can fit 1331 number of Earth in it.
Answer:
Assume Earth and Jupiter to be perfect spheres.
Let radius of Earth be R
e
=R.....................(i)
Radius of Jupiter R
J
=11R......................(ii)
Volume of earth V
e
=
3
4
πR
3
..............(iii)
Volume of Jupiter V
J
=
3
4
πR
J
3
V
J
=
3
4
π(11R)
3
=
3
4
πR
3
×1331..............(iv)
Dividing (iv) by (iii),
V
e
V
J
=
3
4
πR
3
3
4
πR
3
×1331
=1331
Hence, Jupiter can accommodate 1331 earths