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.

Explanation

Here, Volume is changing at a constant rate.

So, `(dV)/dt = k`, where `k` is a constant.

Now, Volume of a sphere, `V = 4/3pir^3`

So, `(dV)/dt = 4/3**3pir^2(dr)/dt`

`=>(dV)/dt = 4pir^2(dr)/dt`

As,`(dV)/dt = k`.So,

`=>kdt = 4pir^2dr`

Now, integrating both sides,

...