A company plans to manufacture lampshades in the shape of a cone from circular pieces of fabric with a radius of $15\text{ in}$. What are the dimensions of the cone with the maximum volume that can be produced?

$r=5\sqrt{3}\text{ in}$, $h=5\sqrt{6}\text{ in}$

$r=5\sqrt{6}\text{ in}$, $h=5\sqrt{3}\text{ in}$

$r=5\sqrt{6}\text{ in}$, $h=\frac{5\sqrt{3}}{2}\text{ in}$

$r=\frac{5\sqrt{6}}{2}\text{ in}$, $h=5\sqrt{3}\text{ in}$