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 $200 \ cm$.

Water is being poured at the rate of $36 \ m^3/min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. The rate at which the water level in the cylinder is rising is:

$A$ ladder $10 \, m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \, cm/sec$. The height of the upper end while it is descending at the rate of $4 \, cm/sec$ is (in $, m$)

$A$ spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute,then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage began is:

The displacement of a particle at time $t$ is given by $x = At^2 + Bt + C$,where $A, B$ and $C$ are constants. If $v$ is the velocity,then $4Ax - v^2 = ....$

The rate of change of the diagonal $R$ of a square with respect to its area $A$ is: