Help with volume formula for elongated sphere of clay

K

Kyria

New member
Joined
Apr 4, 2023
Messages
2
Okay, not sure where to post this question - forgive me if it's in the wrong section. Also, I do not know calc or trig, so symbols from either will probably just confuse me more. This is not a school project, so there are no instructions to go with it, and asking this question on normal math help sites always gets the question rejected saying that they do not do homework... all that said, here's the question

I am trying to work out the formula for this problem...
I have an elongated sphere of clay, I cut that sphere in half... we have the height, base, and density of the clay, so in turn mass and volume can be derived
Now, I add clay to all sides equally, thus whatever amount I add should add 1/2 as much to the height as it does to the base... we have the mass that will be added, and the density is the same as the original clay... is there a formula that will tell me what the final height and base will be?
I didn't really give any numbers here because all of the numbers are variables

I hope the question made sense
 
Kyria said:
is there a formula that will tell me what the final height and base will be?
Click to expand...
Hi Kyria. When you say "final", are you talking about one half only, or will you be joining two augmented pieces together?

spheroid.PNG

The shape in this image is what we call an ellipsoid (in general). With the specific type of ellipsoid shown above, the two line segments labelled b and c have equal length. In other words, if the cut were made along either b or c, then the cross-section (i.e., the flat side) of each half would be a circle with radius b and diameter 2b. Let's say the cut is made that way, for example. The diameter of the cross-section is what you're calling the base measurement, yes?

If the cross-section of your object's half is not a circle, then please let us know.

Kyria said:
I add clay to all sides equally, thus whatever amount I add should add 1/2 as much to the height as it does to the base
Click to expand...
When you say "all sides", are you thinking only of the curved surface? The ratio of height-to-base that you've mentioned implies that you're not adding clay to the flat side.

I'm pretty sure the answer to your question is 'yes'. We just need to work out some details. :)
[imath]\;[/imath]
 
thank you both for responses and for not making me feel foolish for my ignorance in the proper vocabulary
in answer to the questions, yes I was talking about an elipsoid cut in half, so a half-elipsoid? Then by "base" yes, I did mean the diameter of segment b or c. I would not mind having the formula if b&c were different values, however the question itself was running with the presumption that they are equal (a circle). The clay would be added only to the curved surface and finally, when I said "final", I did mean working with only the half-elipsoid, no rejoining
 
You must log in or register to reply here.
Top