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.

(63t+27)^1/3

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

⇒(dv/dt) = k

⇒d/dt (4/3πr³) = k   (Volume of sphere = 4/3πr³)

⇒ (4πr²).dr = kdt

integrating both sides

⇒(4πr³) = 3(kt + C)..................................(i)

at t=0, r=3

C= 36π

at t= 3, r=6

k= 84 π

putting the value of C and k in equation (i)

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

⇒d/dt (4/3πr³) = k