In a frustum of a cone (an upturned cup shape), the top diameter is twice the bottom diameter. If the height of the frustum is h cm, find the height of the cone from which it was cut.
Worked solution (try it first)
Let the full cone have height H.
The small cone cut off has height H−h.
Similar triangles: radius is proportional to distance from the vertex, so H2r=H−hr.