The volume of a cube is increasing at a rate of $9 \text{ cm}^3/\text{s}$. How fast is the surface area increasing when the length of an edge is $10 \text{ cm}$ (in $\text{ cm}^2/\text{s}$)?

$A$ water tank has the shape of an inverted right circular cone,whose semi-vertical angle is $\tan^{-1}(1/2)$. Water is poured in at a constant rate of $5 \ m^3/min$. Then the rate (in $m/min$) at which the level of water is rising at the instant when the depth of water in the tank is $10 \ m$ is:

$A$ spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is $1 \ cm$, the ice-cream melts at the rate of $81 \ cm^3/min$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4\pi} \ cm/min$. The surface area (in $cm^2$) of the chocolate ball (without the ice-cream layer) is: (in $\pi$)

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$, a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground, then:

$A$ bulb is placed at the centre of a circular track of radius $10 \ m$. $A$ vertical wall is erected touching the track at a point $P$. $A$ man is running along the track with a speed of $10 \ m/sec$. Starting from $P$, the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ}$ from $P$ is: (in $m/sec$)

If the radius of a circle increases at the rate of $7 \text{ cm/sec}$,then the rate of increase of its area after $10 \text{ minutes}$ is: