The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

If the surface area of a spherical bubble is increasing at the rate of $4 \text{ cm}^2/\text{sec}$,then the rate of change in its volume (in $\text{cm}^3/\text{sec}$) when its radius is $8 \text{ cm}$ is:

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^o$. At a certain instance,$OA = 8 \ km$,$OB = 6 \ km$ and the ship $A$ is sailing at the rate of $20 \ km/hr$ while the ship $B$ is sailing at the rate of $30 \ km/hr$. Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$):

$A$ particle moves in a straight line so that its velocity at any point is given by ${v^2} = a + bx$,where $a, b \neq 0$ are constants. The acceleration is

$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

The surface area of a spherical ball is increasing at the rate of $4 \pi \,cm^2/s$. The rate at which the radius is increasing when the surface area is $16 \pi \,cm^2$ is: (in $\,cm/s$)