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

$A$ point $P$ is moving on the curve $x^3 y^4 = 2^7$. The $x$-coordinate of $P$ is decreasing at the rate of $8 \text{ units per second}$. When the point $P$ is at $(2, 2)$, the $y$-coordinate of $P$:

If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising is:

If $x$ and $y$ are sides of two squares such that $y = x - x^2$,then the rate of change of area of the second square with respect to that of the first square is

$x$ and $y$ are the sides of two squares such that $y = x - x^{2}$. Find the rate of change of the area of the second square with respect to the area of the first square.

$A$ spherical iron ball of $10 \ cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \ cm^3/min$. When the thickness of ice is $5 \ cm$,then the rate (in $cm/min$) at which the thickness of ice decreases is: