The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

Water is being poured at the rate of $36 \ m^3/min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. The rate at which the water level in the cylinder is rising is:

$A$ point is moving on $y=4-2x^2$. The $x$-coordinate of the point is decreasing at the rate of $5 \text{ units/s}$. Then, the rate at which the $y$-coordinate of the point is changing when the point is at $(1, 2)$ is

$A$ balloon,which always remains spherical,has a variable diameter $\frac{3}{2}(2x+1)$. Find the rate of change of its volume with respect to $x$.

Water is dripping out at a steady rate of $1 \text{ cm}^3/\text{sec}$ through a tiny hole at the vertex of a conical vessel,whose axis is vertical. When the slant height of water in the vessel is $4 \text{ cm}$,find the rate of decrease of the slant height,where the semi-vertical angle of the conical vessel is $\frac{\pi}{6}$.

If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec, then the rate (in units/sec) at which the perimeter of the circle changes, when perimeter is $\sqrt{\pi}$ units, is