If the volume of a spherical ball is increasing at the rate of $4 \pi \, cc/sec$,then find the rate of increase of its radius (in $cm/sec$),when the volume is $288 \pi \, cc$.

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

The radius of a cylinder is increasing at the rate of $3 \, m/sec$ and its altitude is decreasing at the rate of $4 \, m/sec$. The rate of change of volume when the radius is $4 \, m$ and the altitude is $6 \, m$ is:

If the volume of a sphere increases at the rate of $2 \pi \text{ cm}^3/\text{s}$,then the rate of increase of its radius (in $\text{cm}/\text{s}$),when the volume is $288 \pi \text{ cm}^3$,is

The length $x$ of a rectangle is decreasing at the rate of $3 \text{ cm/min}$ and the width $y$ is increasing at the rate of $2 \text{ cm/min}$. When $x = 10 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the area of the rectangle.

The motion of a stone thrown vertically upward is given by $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. Then its velocity at $t = 1$ second is ........ $m/s$.