VIDEO solution: Centimeters per second: All edges of a cube are expanding at a rate of volume changing when each edge is 5 centimeters. (a) How fast is the cm^2/sec changing when each edge is 13 centimeters? How fast is the volume cm^3/sec changing? Need (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "miVPXT4EiinuLmNDtOLZEROaHyj9uf9vXwiwBrQ7fna6sGZ2ZVw8aAqYvToyJfxs"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; if (is_login) { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "miVPXT4EiinuLmNDtOLZEROaHyj9uf9vXwiwBrQ7fna6sGZ2ZVw8aAqYvToyJfxs"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } else { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { anon_pretype(); } else { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "miVPXT4EiinuLmNDtOLZEROaHyj9uf9vXwiwBrQ7fna6sGZ2ZVw8aAqYvToyJfxs"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } } } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "miVPXT4EiinuLmNDtOLZEROaHyj9uf9vXwiwBrQ7fna6sGZ2ZVw8aAqYvToyJfxs", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    VIDEO solution: Centimeters per second: All edges of a cube are expanding at a rate of volume changing when each edge is 5 centimeters. (a) How fast is the cm^2/sec changing when each edge is 13 centimeters? How fast is the volume cm^3/sec changing?

Need (2024)

    FAQs

    How fast is the volume changing in cm3 per sec when each edge is 3 centimeters? ›

    (a) How fast is the volume changing when each edge is 3 cm? Given s = 3 cm and ds/dt = 3 cm/sec, we can differentiate V = s³ with respect to time t to get dV/dt = 3s² ds/dt. Substituting the given values, we get dV/dt = 3*3²*3 = 81 cm³/sec.

    How fast is the surface area of a cube changing when all edges are expanding at a rate of 6 centimeters per second? ›

    The formula for the surface area of a cube is SA = 6s^2. (ds/dt). At a side length of 2 cm, the surface area change rate is 6 * 2 * 2 * 2 = 6 * 4 * 2 = 48 cm^2/s. At a side length of 14 cm, the surface area change rate is 6 * 2 * 14 * 2 = 6 * 28 * 2 = 336 cm^2/s.

    What is the rate of increase of volume of a cube? ›

    The volume of the cube is: V = s^3. The rate of change in volume is dV/dt. The question is asking for the rate that the side length is changing. That would be ds/dt.

    When the edge of a cube is increasing at the rate of 0.05 centimeters? ›

    Given that the edge length (s) is growing at a rate of 0.05 cm/second (i.e., ds/dt = 0.05), substituting this into our equation gives dV/dt = 3s²*0.05. Therefore, the rate of change of the cube's volume with respect to time (in cubic centimeters per second) will be 0.15s² cm³/sec.

    What is a formula for area of cube? ›

    The area of a cube can be found using the formula SA = 6s^2, where SA is the surface area of the cube, in square units, and s is the length of one side of the cube, in units.

    What is the formula for the volume of the cube? ›

    The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times. This results in the formula: Volume = side * side * side. It is often written as V = s * s * s or V = s^3.

    What will happen to the volume of a cube if its edges increased three times? ›

    If the length of each edge of a cube is tripled, what will be the change in its volume? The new volume is 27 times the original volume. ✦ Try This: If the length of each edge of a cube is doubled, what will be the change in its volume? The volume of the cube will increase to 8 times the original volume.

    What is the increase in the surface of the cube if each edge of the cube is increased by 40%? ›

    Calculation: Let the edge of a cube be 100 cm. New edge after increment of 40% = 140 cm. ∴ The percentage increase in surface area is 96%.

    What happens to the surface area volume as the cubes get larger? ›

    Surface area to volume ratio (SA:Vol)

    To help you understand surface to volume ratio, we will use an example of a cube. As the size of the cube increases, the volume will increase more rapidly than the surface area, and the ratio will decrease.

    How to find the rate of change of surface area of a cube? ›

    S(x)=6x2 and V(x)=x3 respectively, with S being the surface, V the volume and x the edge of the cube. By deriving those, we get the functions: S′(x)=12x and V′(x)=3x2 which represent the rate of change (since that's what a derivative essentially is) of the surface and cube.

    What is the fastest way to measure the volume of a cube? ›

    Finding the volume of a cube is a snap - generally, all that's needed is to multiply the cube's length × width × height. Since a cube's sides are all equal in length, another way of thinking of thinking of a cube's volume is s^3, where s is the length of one of the cube's sides.

    What happens to the surface area of a cube as the volume increases? ›

    Similarly when length is tripled (x = 3) surface area is increased ninefold (32 = 9) and volume is increased twenty-sevenfold (33 = 27). The increase in volume is always greater than the increase in surface area. This is true for cubes, spheres, or any other object whose size is increased without changing its shape.

    What happens when each edge of a cube is increased by 20%? ›

    172.8% Each edge of a cube is increased by 20%.

    When each edge of a cube is expanding at the rate of 1 cm? ›

    The rate of the edges expanding, defined as d s d t , affects the volume's rate of change directly. A higher edge rate leads to a more substantial change in volume. When each edge is just 1 centimeter, the volume changes at 9 cubic centimeters per second.

    What happens when the edge of the cube is increased by 50? ›

    ∴ Percentage increase in surface area =125 %.

    What is the volume of the given cube if each edge is 3 cm? ›

    Volume = 3×3×3 = 27 cubic cm.

    What will happen to the volume of a cube if its edge is increased 3 times? ›

    If the length of each edge of a cube is tripled, what will be the change in its volume? The new volume is 27 times the original volume. ✦ Try This: If the length of each edge of a cube is doubled, what will be the change in its volume? The volume of the cube will increase to 8 times the original volume.

    When length of each side of a cube is increased by 3 cm its volume is increased by 2457? ›

    Let s = 15 cm, then s^3 = 3375 cc. Next when the sides are s+3, the volume is (s+3)^3 = 18^3 = 5832 cc. Thus the increase in volume = 5832 - 3375 = 2457 cc.

    How fast is the volume changing when each edge is 2 centimeters? ›

    (a) When each edge is 2 centimeters, the volume is initially 2³ = 8 cm³. If we differentiate both sides with respect to time, we get dV/dt = 3s² ds/dt. Substituting the given values, the rate of volume change when each edge is 2 cm is dV/dt = 3*2²*7 = 84 cm³/sec.

    References

    Top Articles
    Latest Posts
    Article information

    Author: Twana Towne Ret

    Last Updated:

    Views: 5313

    Rating: 4.3 / 5 (44 voted)

    Reviews: 91% of readers found this page helpful

    Author information

    Name: Twana Towne Ret

    Birthday: 1994-03-19

    Address: Apt. 990 97439 Corwin Motorway, Port Eliseoburgh, NM 99144-2618

    Phone: +5958753152963

    Job: National Specialist

    Hobby: Kayaking, Photography, Skydiving, Embroidery, Leather crafting, Orienteering, Cooking

    Introduction: My name is Twana Towne Ret, I am a famous, talented, joyous, perfect, powerful, inquisitive, lovely person who loves writing and wants to share my knowledge and understanding with you.