The volume of a sphere increases at the rate of $\pi \text{ cm}^3/\text{s}$. When the radius is $2 \text{ cm}$,the rate at which the radius increases is . . . . . . $\text{cm/s}$.

The volume of a spherical ball is increasing at a rate of $4 \pi \text{ cm}^3 \text{ s}^{-1}$. The rate at which its radius increases,when its volume is $288 \pi \text{ cm}^3$,is ....... $\text{cm s}^{-1}$.

$A$ man of height $2 \text{ m}$ walks at a uniform speed of $5 \text{ km/h}$ away from a lamp post which is $6 \text{ m}$ high. Find the rate at which the length of his shadow increases. (in $\text{ km/h}$)

$A$ 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 volume of a spherical balloon is increasing at the rate of $30 \ cm^3/min$. Find the rate of change of the surface area of the balloon when its radius is $6 \ cm$.

In a Maha Kumbh, a drone camera is moving along the curve $3y = x^3 - 3$. The camera captures high-quality pictures when the $y$-coordinate changes $9$ times as fast as the $x$-coordinate. Which of the following is a precise position of the drone at that instant?