Q. 194.0( 42 Votes )

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

Answer :

Let the rate of change of the volume of the balloon be k. (k is a constant)


Or,





Integrating both sides,




Now, given that


At t = 0, r = 3:


4π × 33 = 3(k×0 + c)


108π = 3c


c = 36π


At t = 3, r = 6:



k = 84π


Substituting the values of k and c in i)






So the radius of balloon after t seconds is


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