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.
Answer & explanation
Correct answer: option 2
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