My Math Forum Height of a sphere cap

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 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: 7,945 Thanks: 1136 Math Focus: Elementary mathematics and beyond $\displaystyle h=r-\sqrt{r^2-a^2}$ 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 $\displaystyle h=r+\sqrt{r^2-a^2}$ 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
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Quote:
 Originally Posted by foothill I am trying to figure out the height of a sphere cap, with volume, and radius of the cap provided.
Thus my post.

October 30th, 2014, 11:26 PM   #5
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Quote:
 Originally Posted by greg1313 Thus my post.
oops, my bad. So I only have the cap volume and radius of the sphere, but not the radius of the cap.

Thanks for the reminder.

 October 31st, 2014, 12:00 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,945 Thanks: 1136 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
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Quote:
 Originally Posted by greg1313 I would imagine that the solution is complicated; see here.
or see:
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