Question

sunita ia curious to find out the relationship between the diameter of the Jupiter and the earth . from the data available it is known that the volume of Jupiter is 729 times the volume of Earth. she concluded that the diameter of Jupiter is 9times the diameter of Earth. justify her statement by prooving it and find the ratios of their surface arras

Answer 1

let d is the diameter of earth .
so, diameter of jupiter =9d

we know ,
volume of spherical body=(4/3)pi.r^3
diameter =2 x radius
so,
volume of spherical body=(4/3)pi. (d/2)^3
=(1/6)pi.d^3
now,
volume of earth = (1/6)pi.d^3
volume of jupiter =(1/6)pi. (9d)^3=(729)(1/6)pi.d^3

divide both
volume of earth/volume of Jupiter=1/729
volume of Jupiter =729 x volume of earth .

here we see and we can say that statement is correct.

Answer 2

Given, diameter of Jupiter is 9times the diameter of earth
so,that let
diameter of the earth =d1
diameter of the Jupiter =d2
therefore d2= 9×d1
we know that r= d/2
we know that volume of sphere = 4/3 πr^3

volume of the earth =4/3 πr1^3
= 4/3×π(d1/2)^3
=1/6 πd1^3
volume of the Jupiter = 4/3 πr2^3
= 4/3 π( d2/2)^3
= 1/6× π (9×d1)^3
=729/6×π×d1^3
Divide , volume of the Jupiter and volume of the earth
we have got this,
therefore ,volume of the Jupiter= 729× volume of the earth .