The volume of a 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 the balloon after t seconds.

Question

Philoid · Accepted Answer

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

Find: Find the radius of the balloon after t second.

=

Integrating both sides, we get:

=

= .....(i)

Now, at t = 0, r = 3.

=

= C = 36

At t = 3, r = 6:

=

= k = 84π

Substitute the value of K and C in equation (1), we get

=

= r³ = 63t + 27

= r = (63t + 27)^1/3

Hence, the radius of the balloon after t seconds is (63 t + 27)^1/3 .