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# Frustrating frustum

Posted 10 years ago
 I'm chairman of a lighthouse non-profit. We own a brick caisson lighthouse whose form is that of a frustum 22 feet in diameter at the base and 21 feet in diameter at a height of 24 feet above the base. I'm trying to calculate the height of the resulting cone if the intersecting plane at the top were removed. Anyone have a suggestion? None of my queries, and I've tried many, produce anything that seems to be relevant.
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Posted 10 years ago
 Thank you. I figured the missing portion of the cone would figure into the solution, just wasn't sure how to relate the two. Great help!
Posted 10 years ago
 The two right angled triangles pictured are similar, so their corresponding side length ratios are the same, in other words (H-h)/H == r/R.
Posted 10 years ago
 Ilian,Thanks. If I understand the solution you've presented, the cone is approximately 528 feet high. Since I'm not a mathematician and only last night started playing with Mathematica 9 trial, some of the syntax is unfamiliar. Can you give me a simple explanation as to what you did?
Posted 10 years ago
 In[3]:= Solve[(H - 24)/H == 21/22, H] Out[3]= {{H -> 528}}