SOLUTION: a cylinder of height h cm and radius r cm stands on a table. a cone of height H cm is placed over the cylinder and the rests on the table wit the top of the cylinder touching the i

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Question 407197: a cylinder of height h cm and radius r cm stands on a table. a cone of height H cm is placed over the cylinder and the rests on the table wit the top of the cylinder touching the inside of the cone. the ratio r:R is 2:5
use the given ratio to write an expression for r in terms of R
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
r%2FR+=+2%2F5 ==> r+=+%282%2F5%29R
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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%2F%28R+-+r%29+=+%28H+-+h%29%2Fr
==> hr+=+%28H+-+h%29%28R+-+r%29
<==> hr+=+HR+-+Hr+-+hR++%2Bhr
<==> Hr+=+%28H+-+h%29R
<==> r+=+%28%28H+-+h%29%2FH%29R
then use r+=+%282%2F5%29R to find a relationship between h and H.