If a man of height $1.8 \ m$ is walking away from the foot of a light pole of height $6 \ m$ with a speed of $7 \ km/h$ on a straight horizontal road,then the rate of change of the length of his shadow is (in $km/h$):

Coffee is draining from a conical filter,with both height and diameter equal to $15 \, cm$,into a cylindrical coffee pot with a diameter of $15 \, cm$. The rate at which coffee drains from the filter into the pot is $100 \, cm^3/min$. The rate in $cm/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \, cm$ deep,is:

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=4 \, cm$. (in $\pi \, cm$)

Gas is being pumped into a spherical balloon at the rate of $30 \, ft^3/min$. The rate at which the radius increases when it reaches the value $15 \, ft$ is:

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$, then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$, is in $\text{cm}^2\text{/sec}$: (in $\pi$)

If the rate of increase of the area of a circle is not constant but the rate of increase of the perimeter is constant,then the rate of increase of the area varies: