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

volume of jupiter is 729 times volume of earth
let diameter of jupiter is d1
let diameter of earth is d2
then, πd1³/6 = 729×πd2³/6
          d1³ = 729×d2³
          d1³ = (9×d2)³
          d1 = 9×d2
hence proved that diameter of jupiter is 9 times diameter of earth
ratio of surface areas of jupiter to earth is
πd1²/πd2² = d1²/d2²
                   = (9×d2)²/d2²
                   = 81/1
therefore the required ratio is 81:1    

Answer 2

volume = 4/3 π R³        
  Radius of Earth = R2   Radius of Jupiter R1

So     4/3 π R1³ :   4/3 π R2³ = 721 : 1 =  9³  : 1³
             So   R1 :   R2 =  9 : 1
          So the ratio of diameters is also 9 : 1

Surface area : 4 πR²....
            Ratio:     R1² : R2² =  9² :  1² =  81 : 1