Question

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.

Answer 1

Let r be the radius and V be the volume of the spherical balloon at any time t.

Then the rate of change in volume of the spherical balloon is dV/dt which is a constant.

Integrating both sides, we get

Initially the radius is 3 units

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