Volume of Water Inside a Cup
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 '18 at 11:22
user618548
1
add a comment |
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 '18 at 11:22
user618548
1
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27
add a comment |
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 '18 at 11:22
user618548
1
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
integration volume
asked Nov 22 '18 at 11:22
user618548
1
asked Nov 22 '18 at 11:22
user618548
1
asked Nov 22 '18 at 11:22
user618548
1
asked Nov 22 '18 at 11:22
user618548
1
asked Nov 22 '18 at 11:22
user618548
1
1
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27
add a comment |
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27
add a comment |
1 Answer
1
active
oldest
votes
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
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',
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%2f3009017%2fvolume-of-water-inside-a-cup%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
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
add a comment |
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
add a comment |
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
answered Nov 22 '18 at 11:27
TonyK
41.7k353132
41.7k353132
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%2f3009017%2fvolume-of-water-inside-a-cup%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
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 '18 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 '18 at 11:27