Gas is being pumped into a spherical balloon at the rate of $30 \, ft^3/min$. The rate at which the radius increases when it reaches the value $15 \, ft$ is:

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 radius of a cylinder is increasing at a rate of $3 \text{ m/s}$ and its height is decreasing at a rate of $4 \text{ m/s}$. Find the rate of change of its volume when the radius is $4 \text{ m}$ and the height is $6 \text{ m}$.

Let $S$ be the focus of $y^2 = 4x$ and a point $P$ is moving on the curve such that its abscissa is increasing at the rate of $4 \text{ units/sec}$. Then the rate of increase of the projection of $SP$ on the line $x + y = 1$ when $P$ is at $(4, 4)$ is:

The length $x$ of a rectangle is decreasing at the rate of $5 \text{ cm/min}$ and the width $y$ is increasing at the rate of $4 \text{ cm/min}$. When $x = 8 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the area of the rectangle.

Displacement $s$ of a particle at time $t$ is expressed as $s=2 t^3-9 t$. Find the acceleration at the time when the velocity vanishes.