Question 407197
{{{r/R = 2/5}}} ==> {{{r = (2/5)R}}}

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On a related note, you can actually find a relationship between h and H:

A vertical cross-section passing through the apex of the cone produces two similar right triangles:
The top triangle has horizontal leg r and vertical leg H - h.
The bottom triangle has horizontal leg R - r and vertical leg h.  Hence
by similarity of triangles,

{{{h/(R - r) = (H - h)/r}}}
==> {{{hr = (H - h)(R - r)}}}
<==> {{{hr = HR - Hr - hR  +hr}}}
<==> {{{Hr = (H - h)R}}}
<==> {{{r = ((H - h)/H)R}}}

then use {{{r = (2/5)R}}} to find a relationship between h and H.