Q15 of 37 Page 195

Volume of a sphere varies directly with cube of length of its radius and surface area of sphere varies directly with the square of the length of radius. Let us prove that the square of volume of sphere varies directly with cube of its surface area.

Given:

Acc. To given conditions:


Volume of sphere ∝ (radius)3


V ∝ (r)3


V = k (r)3 ….(1)


Surface area of sphere ∝ (radius)2


S ∝ (r)2


S = m (r)2




Put the value of r in (1)




Square on both sides,




Where k and m are non zero constants.


So,


v2∝ s3


hence proved.


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