Math Is Fun Forum

manich44

Member

Registered: 2009-11-29

Posts: 14

How do I calculate the height of a sphere cap?

Hi,

I know how to find the volume of a sphere when height and radius is given but how do I go about calculating the height of a sphere cap if only the volume and radius of sphere cap are given? I know its a cubic equation but dont know how to do this.

Thanks....Mark

r = 5.4  V=160 in this instance

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: How do I calculate the height of a sphere cap?

Do you know how to do volumes of revolution?
If not, use the formula for the volume of a cap here http://mathworld.wolfram.com/SphericalCap.html to solve for h.

If yes, you can derive it yourself, or see the general derivation here http://mathworld.wolfram.com/SphericalSegment.html

manich44

Member

Registered: 2009-11-29

Posts: 14

Re: How do I calculate the height of a sphere cap?

Hi,
Thanks for the reply,

Had a look at the mathworld page,not sure where to start though,this is my first attempt.

Mark

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: How do I calculate the height of a sphere cap?

On the mathworld page it gives

You're given

,

So you can solve for h.

If you want to derive the formula you need to know about integral calculus and volumes of revolution

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How do I calculate the height of a sphere cap?

Hi identity;

h = 3.13941177833...

With the other 2 roots being complex.

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If it ain't broke, fix it until it is.
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