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August 25th, 2008, 03:17 AM   #1
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Prolate spheroid surface area calculation problems

Hi, I'm doing a research project at medical school and am trying to quantify bone loss - the lesion can be approximated to a spheroid and I'd like to find its surface area. If the semi-major axis = 5.625 and the semi-minor axis = 3.4, an online example shows the SA should be ~142.3. ( ... olids.html)

However, I've input 2 different formulas to calculate SA into MS excel and got the same answer both times (211.6666599)

The 2 formulas I've used are (D4=semi-major axis, C4=semi-minor axis, N4=ACOS(C4/D4), Q4=SQRT((1-POWER(C4,2)/POWER(D4,2))) ):

Surface area =2*PI()*((POWER(C4,2))+(C4*D4*N4)/(SIN(N4)))


Surface Area =2*PI()*(POWER(C4,2)+D4*C4*ASIN(Q4)/Q4)

I obtained the second formula from:, which appears to be a reputable website and since I'm getting the same answer in 2 different ways now, I'm at a loss as to what's going on!

I'm not sending this because I'm lazy - I've spent hours on this and this is a last resort so I'd be incredibly grateful for your help!


The University of Edinburgh
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August 25th, 2008, 01:27 PM   #2
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Re: Prolate spheroid surface area calculation problems

Just a suggestion: switch the axes in the formulas you are using and see what you get.
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