Mixing
Cutting cork for three different holes
$begingroup$
A cork of circular base, radius 1 unit and height of 2 units can be carved to snugly fit into square, circular and triangular holes. What is the volume of the smallest shape that can fit and what is the volume of the largest shape? I don't know how to calculate these volumes either with pre-calculus or calculus methods.
calculus euclidean-geometry
asked Feb 1 at 19:08
user519651user519651
11
$endgroup$
add a comment |
$begingroup$
A cork of circular base, radius 1 unit and height of 2 units can be carved to snugly fit into square, circular and triangular holes. What is the volume of the smallest shape that can fit and what is the volume of the largest shape? I don't know how to calculate these volumes either with pre-calculus or calculus methods.
calculus euclidean-geometry
asked Feb 1 at 19:08
user519651user519651
11
$endgroup$
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
1
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39
add a comment |
$begingroup$
A cork of circular base, radius 1 unit and height of 2 units can be carved to snugly fit into square, circular and triangular holes. What is the volume of the smallest shape that can fit and what is the volume of the largest shape? I don't know how to calculate these volumes either with pre-calculus or calculus methods.
calculus euclidean-geometry
asked Feb 1 at 19:08
user519651user519651
11
$endgroup$
A cork of circular base, radius 1 unit and height of 2 units can be carved to snugly fit into square, circular and triangular holes. What is the volume of the smallest shape that can fit and what is the volume of the largest shape? I don't know how to calculate these volumes either with pre-calculus or calculus methods.
calculus euclidean-geometry
calculus euclidean-geometry
asked Feb 1 at 19:08
user519651user519651
11
asked Feb 1 at 19:08
user519651user519651
11
asked Feb 1 at 19:08
user519651user519651
11
asked Feb 1 at 19:08
user519651user519651
11
asked Feb 1 at 19:08
user519651user519651
11
11
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
1
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39
add a comment |
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
1
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
1
1
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39
add a comment |
0
active
oldest
votes
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',
autoActivateHeartbeat: false,
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%2f3096616%2fcutting-cork-for-three-different-holes%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
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%2f3096616%2fcutting-cork-for-three-different-holes%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
$begingroup$
Isn't the minimun (or rather infimum) volume just zero?
$endgroup$
– Hagen von Eitzen
Feb 1 at 19:38
1
$begingroup$
See math.stackexchange.com/questions/1947363
$endgroup$
– cgiovanardi
Feb 1 at 23:05
$begingroup$
What does the "... shape that can fit" fit?
$endgroup$
– William Elliot
Feb 2 at 2:09
$begingroup$
It wouldn't be a cork then!
$endgroup$
– user519651
Feb 2 at 16:39