A balloon is inflated, and its volume in cubic meters after $t$ seconds is given by the function $V\left(t\right)=4t$. Calculate $V^{\prime}\left(10\right)$ and interpret the meaning of this value. Include units in your answer.

A square's sides are shrinking at a constant rate of $2\text{ cm/s}$. What is the rate at which the length of the square's diagonal is changing?

Avogadro's law states that for a given temperature and pressure, the volume $V$ (in liters) and the number of moles $n$ of a gas are directly proportional, given by the equation $V=kn$, where $k>0$ is a constant. Suppose the volume of a gas is increasing at a rate of $0.3\text{ L/min}$ when the volume $V=5\text{ L}$ and the number of moles is $n=1\text{ mol}$. Determine the rate at which the number of moles is changing at this moment.

Determine the rate of change of the radius of a soap bubble if its volume increases at a rate of $20{\text{ cm}}^3\text{/min}$. The radius of the bubble is $5\text{ cm}$.

A right cone's lateral surface area $L$ is given by the equation $L=\pi r\sqrt{h^2+r^2}$, where $r$ is the base radius and $h$ is the height. If $r$ is constant, how is $\frac{dL}{dt}$ related to $\frac{dh}{dt}$?