Sunita is 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 the earth. She concluded that the diameter of the jupiter is 9 times the diameter of the earth.
(a) Justify her statement by proving it and find the ratio of their surface areas.
(b) Which value is depictedby sunita by concluding the experiment?
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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
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
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