The rate of change of the radius of a sphere is $0.1 \ cm/s$. Find the rate of change of its surface area when its radius is $200 \ cm$.

The radius of a cylinder is increasing at the rate of $5 \ cm/min$,so that its volume remains constant. When its radius is $5 \ cm$ and height is $3 \ cm$,the rate of decrease of its height is .......... $cm/min$.

In a $\triangle ABC$,the sides $b$ and $c$ are fixed. If there is an error of $\delta A$ in measuring angle $A$,then the percentage error in measuring the length of the side $a$ is:

If the radius of a circle increases at the rate of $7 \text{ cm/sec}$,then the rate of increase of its area after $10 \text{ minutes}$ is:

The rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$ 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 $km/hr$):