$A$ spherical balloon is expanding. If at any instant the rate of increase of its volume is $16$ times the rate of increase of its radius,then its radius at that instant is:

Water is running into a hemispherical bowl of radius $180 \text{ cm}$ at the rate of $108 \text{ cubic decimetres per minute}$. How fast is the water level rising when the depth of the water level in the bowl is $120 \text{ cm}$? $(1 \text{ decimetre} = 10 \text{ cm})$

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 $km/hr$):

If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec,then the rate (in units/sec) at which the perimeter of the circle changes,when perimeter is $\sqrt{\pi}$ units,is

If the volume of a spherical balloon is increasing at the rate of $900 \ cm^3/sec$,then find the rate of change of the radius of the balloon at the instant when the radius is $15 \ cm$ (in $cm/sec$).

$A$ stone is falling freely and describes a distance $s$ in $t$ seconds given by the equation $s = \frac{1}{2}g{t^2}$. The acceleration of the stone is