February 10th, 2017, 08:11 AM  #1 
Newbie Joined: Feb 2017 From: Finland Posts: 2 Thanks: 0  Surface area of a prolate spheroid
Hello guys! I'm trying to calculate the surface area of a prolate spheroid and I found this formula from Prolate Spheroid  from Wolfram MathWorld image.jpg However, I haven't been able to proof that r(z)(1+r'(z)^2)^1/2 = a(1+((ac)(a+c)z^2)/c^4)^1/2 I know the left side is just derivated and solved algebraically but I still don't manage to proof it. I would be very grateful if someone could help me! 
February 11th, 2017, 09:12 AM  #2 
Member Joined: Feb 2015 From: Southwest Posts: 96 Thanks: 24 
I got $\displaystyle r'(z)=\frac{az}{c^2\sqrt{1(\frac{z}{c})^2}}$ $\displaystyle r'(z)^2=\frac{a^2z^2}{c^4c^2z^2}$ Then I tried inserting all that into the integrand, but I got lost in it. I'm hoping my failed work triggers success in yours. $\displaystyle r(z)\sqrt{1+r'(z)^2}=a\sqrt{(1\frac{z^2}{c^2})(1+\frac{a^2z^2}{c^4c^2z^2})}$ $\displaystyle r(z)\sqrt{1+r'(z)^2}=a\sqrt{1+\frac{a^2z^2}{c^4c^2z^2}\frac{z^2}{c^2}\frac{a^2z^4}{c^6c^4z^2}}$ $\displaystyle r(z)\sqrt{1+r'(z)^2}=a\sqrt{1+\frac{c^2a^2z^2}{c^6c^4z^2}\frac{c^4z^2c^4z^4}{c^6c^4z^2}\frac{a^2z^4}{c^6c^4z^2}}$ This is where I got stuck. 
February 26th, 2017, 01:13 AM  #3 
Newbie Joined: Feb 2017 From: Finland Posts: 2 Thanks: 0 
Thanks for your help! Later on I realized if I take common factors and cancell some stuff I will get the correct form


Tags 
area, prolate, spheroid, surface 
Search tags for this page 
prolate spheroid surface area,formula for calculating the surface area of prolate spheroid,proof of surface area of a prolate spheriod
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
surface area  Kinroh  Physics  2  January 16th, 2014 04:14 PM 
Area of a surface  renatus  Calculus  1  May 23rd, 2009 07:33 AM 
Surface Area  sansar  Calculus  2  April 17th, 2009 05:17 PM 
Prolate spheroid surface area calculation problems  supdoc  Algebra  1  August 25th, 2008 01:27 PM 
Box Surface Area  symmetry  Algebra  5  February 3rd, 2007 06:09 PM 