A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of the silo (including the part inside the roof section) is 12000 $\textrm{ft}^3$ and the cylindrical part is 40 ft tall, what is the radius of the silo?

Note: The following formulas may be useful:
$$\mbox{Volume of a Cylinder } = \pi r^2 h$$ $$\mbox{Volume of a Sphere } = \frac{4}{3} \pi r^3$$
Radius $=$ ft