[(way)OT] Formula for volume of a circular lens with an elliptical profile?

BrowserUk has asked for the wisdom of the Perl Monks concerning the following question:

Usual reasons: a) I've looked in all the usual places; b) we usually get quicker, better answers here than other places. (If it mitigates, the calculation will be performed by a Perl script.)

Given (R)adius and (T)hickness (major and minor axes), the foci are at ((R/2)² - (T/2)²)^-2, and the area is πRT.

Is the volume as simple as: π²RT?

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I knew I was on the right track :)

In the absence of evidence, opinion is indistinguishable from prejudice.

Comment on [(way)OT] Formula for volume of a circular lens with an elliptical profile?

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Re: [(way)OT] Formula for volume of a circular lens with an elliptical profile? by RichardK (Parson) on Sep 27, 2016 at 23:37 UTC
I'm not quite sure what your lens looks like, but is it half of an ellipsoid ? where ellipsoid volume V= 4/3 π abc	[reply]
Re^2: [(way)OT] Formula for volume of a circular lens with an elliptical profile? by BrowserUk (Patriarch) on Sep 28, 2016 at 03:57 UTC
is it half of an ellipsoid ? Thanks for the link, I had never heard of an ellipsoid. Reading further, it seems that the terms: ellipsoid of revolution and spheroid are specific version of an ellipsoid, and what I was trying to describe is properly terms an "oblate spheroid". Which has the simpler volume formula given by anonymonk below (or above). With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday' Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. "Science is about questioning the status quo. Questioning authority". I knew I was on the right track :) In the absence of evidence, opinion is indistinguishable from prejudice.	[reply]
Re^3: [(way)OT] Formula for volume of a circular lens with an elliptical profile? by Aldebaran (Curate) on Sep 28, 2016 at 11:51 UTC
The oblate spheroid is how r is described for earth, with naive to pretty-good mathematical assumptions regarding dynamics. A person could integrate over this spheroid as opposed to flattening it to calculate its volume. I say that as a rebuke to those in my own country who have announced their willingness to take the whole pumpkin and flatten it, like their flat earth views on almost everything, not on those who deform space to solve problems. And now we're being hit with pumpkin spice everything, and it's not like one can avoid it, much like the sun....	[reply]
Re: [(way)OT] Formula for volume of a circular lens with an elliptical profile? by Anonymous Monk on Sep 27, 2016 at 23:31 UTC
It's just a sphere that's squashed in one dimension. 4/3 pi R^2 T	[reply]
Re^2: [(way)OT] Formula for volume of a circular lens with an elliptical profile? by BrowserUk (Patriarch) on Sep 28, 2016 at 03:52 UTC
a sphere that's squashed in one dimension. Indeed. Thank you. With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday' Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. "Science is about questioning the status quo. Questioning authority". I knew I was on the right track :) In the absence of evidence, opinion is indistinguishable from prejudice.	[reply]


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