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

Let a kind of bacteria grow following the function $f(t) = t^4$,where $t$ is given in seconds. If the rate of growth of the bacteria after $t_0$ seconds is $4000 \text{ units/second}$,then $t_0 =$

Find the rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$.

$A$ spherical balloon is being inflated at the rate of $35 \, cm^3/min$. The rate of increase in the surface area (in $cm^2/min$) of the balloon when its diameter is $14 \, cm$,is

If $V = \frac{4}{3}\pi r^3$,find the rate of change of $V$ with respect to $t$ when $r = 10$ and $\frac{dr}{dt} = 0.01$.

The rate of change of the area of a circle with respect to its radius $r$ at $r = 6 \text{ cm}$ is