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October 30th, 2014, 03:28 PM   #1
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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*ℎ^2)/3] *(3r−ℎ)

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!
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October 30th, 2014, 05:22 PM   #2
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$\displaystyle h=r-\sqrt{r^2-a^2}$ 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
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October 30th, 2014, 06:36 PM   #3
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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.
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October 30th, 2014, 11:16 PM   #4
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Quote:
Originally Posted by foothill View Post
I am trying to figure out the height of a sphere cap, with volume, and radius of the cap provided.
Thus my post.
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October 30th, 2014, 11:26 PM   #5
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Originally Posted by greg1313 View Post
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.
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October 31st, 2014, 12:00 AM   #6
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Then you are left with a cubic function in terms of h. I would imagine that the solution is complicated; see here.
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October 31st, 2014, 10:19 PM   #7
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Quote:
Originally Posted by greg1313 View Post
I would imagine that the solution is complicated; see here.
or see:
S.O.S. Mathematics CyberBoard • View topic - Height of a sphere cap
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