General Formula for Volume of a Torus with different shaped cross sections
up vote
0
down vote
favorite
The formula for the volume of a torus is $(pi r^2) times 2pi R$. Does the formula (area of the cross-section) $ times 2pi R$ generalize to the volume of all tori? And is there a proof for it (doesn't have to be rigorous).
calculus analytic-geometry
asked Nov 22 at 5:47
Muchang Bahng
562
add a comment |
up vote
0
down vote
favorite
The formula for the volume of a torus is $(pi r^2) times 2pi R$. Does the formula (area of the cross-section) $ times 2pi R$ generalize to the volume of all tori? And is there a proof for it (doesn't have to be rigorous).
calculus analytic-geometry
asked Nov 22 at 5:47
Muchang Bahng
562
1
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The formula for the volume of a torus is $(pi r^2) times 2pi R$. Does the formula (area of the cross-section) $ times 2pi R$ generalize to the volume of all tori? And is there a proof for it (doesn't have to be rigorous).
calculus analytic-geometry
asked Nov 22 at 5:47
Muchang Bahng
562
The formula for the volume of a torus is $(pi r^2) times 2pi R$. Does the formula (area of the cross-section) $ times 2pi R$ generalize to the volume of all tori? And is there a proof for it (doesn't have to be rigorous).
calculus analytic-geometry
calculus analytic-geometry
asked Nov 22 at 5:47
Muchang Bahng
562
asked Nov 22 at 5:47
Muchang Bahng
562
asked Nov 22 at 5:47
Muchang Bahng
562
asked Nov 22 at 5:47
Muchang Bahng
562
asked Nov 22 at 5:47
Muchang Bahng
562
562
1
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52
add a comment |
1
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52
1
1
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
A torus always have a circular cross section.
See this https://en.wikipedia.org/wiki/Torus
answered Nov 22 at 6:43
Dikshit Gautam
795
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3008780%2fgeneral-formula-for-volume-of-a-torus-with-different-shaped-cross-sections%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
A torus always have a circular cross section.
See this https://en.wikipedia.org/wiki/Torus
answered Nov 22 at 6:43
Dikshit Gautam
795
add a comment |
up vote
0
down vote
A torus always have a circular cross section.
See this https://en.wikipedia.org/wiki/Torus
answered Nov 22 at 6:43
Dikshit Gautam
795
add a comment |
up vote
0
down vote
up vote
0
down vote
A torus always have a circular cross section.
See this https://en.wikipedia.org/wiki/Torus
answered Nov 22 at 6:43
Dikshit Gautam
795
A torus always have a circular cross section.
See this https://en.wikipedia.org/wiki/Torus
answered Nov 22 at 6:43
Dikshit Gautam
795
answered Nov 22 at 6:43
Dikshit Gautam
795
answered Nov 22 at 6:43
Dikshit Gautam
795
answered Nov 22 at 6:43
Dikshit Gautam
795
795
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3008780%2fgeneral-formula-for-volume-of-a-torus-with-different-shaped-cross-sections%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
Pappus's centroid theorem
– achille hui
Nov 22 at 5:52