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:

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 $6 \ cm$.

Water is being poured into a cylindrical vessel with a radius of $2 \text{ cm}$ at a rate of $8 \text{ cm}^3/\text{s}$. The rate at which the height of the water is increasing is:

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho} \frac{d \rho}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

$A$ balloon which always remains spherical is being inflated by pumping in $10 \text{ cm}^3$ of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15 \text{ cm}$.

$A$ cube of ice melts without changing its shape at a uniform rate of $4 \, cm^3/min$. The rate of change of the surface area of the cube,in $cm^2/min$,when the volume of the cube is $125 \, cm^3$,is: