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

$A$ right circular cone has height $9 \text{ cm}$ and radius of base $5 \text{ cm}$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $\frac{\pi}{A} \text{ cm/sec}$, where $A$ is the area of the water surface at that instant, then the cone is completely filled in: (in $\text{ sec}$)

The radius of a circle is increasing at a rate of $0.1 \text{ cm s}^{-1}$. Then the rate of change of area,when its radius is $5 \text{ cm}$,is .........

The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm s}^{-1}$. How fast does its area increase when its side is $10 \text{ cm}$?