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Frustrating frustum

Keith Thompson
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.
POSTED BY: Keith Thompson
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Keith Thompson
Keith Thompson
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 BY: Keith Thompson

enter image description here

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 BY: Ilian Gachevski
Keith Thompson
Keith Thompson
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 BY: Keith Thompson

In[3]:= Solve[(H - 24)/H == 21/22, H]

Out[3]= {{H -> 528}}
POSTED BY: Ilian Gachevski
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