Volume and surface area of solids

A solid ornament is made by joining a hemisphere of radius 5 cm to a cone of the same radius. The total volume of the ornament is $220\pi \,\text{cm}^3$. Find the height of the cone, $h$, in cm.

(Take volume of cone as $\tfrac{1}{3}\pi r^2 h$ and volume of hemisphere as $\tfrac{2}{3}\pi r^3$.)