October 30th, 2014, 03:28 PM  #1 
Newbie Joined: Oct 2014 From: Brisbane Posts: 5 Thanks: 0  Height of a sphere cap
I am trying to figure out the height of a sphere cap, with volume, and radius of the cap provided. I know I can figure the height with the below formula: V=[(pie*â„Ž^2)/3] *(3râˆ’â„Ž) However, I am having a hard time to solve it since I cannot deal with the h^2 Is there any other more straightforward way to solve for height? Thanks! 
October 30th, 2014, 05:22 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
$\displaystyle h=r\sqrt{r^2a^2}$ where $r$ is the radius of the sphere and $a$ is the radius of the cap. If you're concerned with a cap that takes up more than half the sphere, then $\displaystyle h=r+\sqrt{r^2a^2}$ Spherical cap  Wikipedia, the free encyclopedia 
October 30th, 2014, 06:36 PM  #3 
Newbie Joined: Oct 2014 From: Brisbane Posts: 5 Thanks: 0 
But "a" is not known in my case, and I only have the cap volume and the radius of the sphere. So I think yours is not applicable.

October 30th, 2014, 11:16 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  
October 30th, 2014, 11:26 PM  #5 
Newbie Joined: Oct 2014 From: Brisbane Posts: 5 Thanks: 0  
October 31st, 2014, 12:00 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
Then you are left with a cubic function in terms of h. I would imagine that the solution is complicated; see here.

October 31st, 2014, 10:19 PM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,329 Thanks: 1024  Quote:
S.O.S. Mathematics CyberBoard â€¢ View topic  Height of a sphere cap  

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