Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \text{ cm}$.

$A$ sphere increases its volume at the rate of $\pi \text{ cm}^3/\text{s}$. The rate at which its surface area increases when the radius is $1 \text{ cm}$ is

The distance $s$ (in meters) covered by a particle in $t$ seconds is given by $s = ae^t + \frac{b}{e^t}$. Then the acceleration of the particle at time $t$ is:

$A$ spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute,then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage began is:

The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.