If a spherical balloon has a variable diameter $d = 3x + \frac{9}{2}$ units, then the rate of change of its volume $V$ with respect to $x$ is:

The radius of the base of a cone is increasing at the rate $3 \text{ cm/min}$ and the altitude is decreasing at the rate $4 \text{ cm/min}$. The rate at which the lateral surface area is changing,when the radius is $7 \text{ cm}$ and altitude is $24 \text{ cm}$,is:

If the rate of change of the area of a square $S$ is equal to its side length,and the rate of change of the side of $S$ is the same as that of a cube $C$,then the rate of change of the volume of $C$,at the time when its side length is $2$ units,will be ............ $units^3/sec$.

The rate of change of the volume of a sphere with respect to its surface area,when the radius is $5 \ m$ is

$A$ balloon,which always remains spherical,has a variable radius. Find the rate at which its volume is increasing with respect to its radius when the radius is $10 \text{ cm}$.

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 $6 \ cm$.