The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm/sec}$. The rate at which the area increases,when the side is $10 \text{ cm}$,is

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

$A$ rod of length $41 \ ft$ with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \ ft/min$. When the end $B$ is at a height of $9 \ ft$ from the floor,the rate at which the area of the triangle formed by the rod with the wall and the floor changes at that instant is (in $ft^2/min$):

$A$ ladder $5 \ m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/sec$. How fast is its height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?

The distance $s$ in meters covered by a body in $t$ seconds is given by $s = 3t^2 - 8t + 5$. The body will stop after

Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3 \text{ cm}$. (in $\pi \text{ cm}$)