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

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

$A$ ladder is resting against a wall at an angle of $30^\circ$ with the wall. $A$ man is ascending the ladder at the rate of $3 \, ft/sec$. His rate of approaching the wall is:

$A$ stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of $5 \ cm/sec$. The rate at which the area increases after $2 \ seconds$ is:

$A$ particle moves along the curve $y = x^2 + 2x$. At what point on the curve do the $x$ and $y$ coordinates of the particle change at the same rate?

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