The rate of change of the volume of a sphere with respect to its surface area,when the radius is $5 \ m$ is

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

The height of a right circular cylinder is decreasing while its diameter is increasing at a rate of $4 \text{ cm/s}$ so as to keep its volume unchanged. The rate of change in its lateral surface area (in $\text{cm}^2/\text{s}$) at the instant when its diameter is $8 \text{ cm}$ and height is $12 \text{ cm}$,is (in $\pi$)

$A$ 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 $ft^2/min$):

The volume of a spherical balloon is increasing at the rate of $2 \ cm^3/sec$. When its radius is $4 \ cm$,the rate of change of its surface area (in $cm^2/sec$) is

The side of an equilateral triangle expands at the rate of $2 \, cm/s$. The rate of increase of its area when each side is $10 \, cm$ is: