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.

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

20