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 $\frac{dh}{dt}$?

$\frac{dL}{dt}=\frac{2\pi rh}{\sqrt{h^2+r^2}}\frac{dh}{dt}$

$\(\frac{d L}{d t}\)=\(\frac{\pi r h}{\sqrt{h^2+r^2}\)}\(\frac{d h}{d t}\)$

$\frac{dL}{dt}=2\pi r^{2}h\sqrt{h^2+r^2}\frac{dh}{dt}$

$\frac{dL}{dt}=\pi r^{2}h\sqrt{h^2+r^2}\frac{dh}{dt}$