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{"version":3,"file":"6M30-R3H16QCA.js","sources":["../../src/exercices/6e/6M30.js"],"sourcesContent":["import { combinaisonListes, choice } from '../../lib/outils/arrayOutils'\nimport { deprecatedTexFraction } from '../../lib/outils/deprecatedFractions.js'\nimport { nombreDeChiffresDansLaPartieEntiere } from '../../lib/outils/nombres.js'\nimport { sp } from '../../lib/outils/outilString.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport Decimal from 'decimal.js'\nimport { context } from '../../modules/context.js'\nimport { gestionnaireFormulaireTexte, listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { propositionsQcm } from '../../lib/interactif/qcm.js'\nimport Grandeur from '../../modules/Grandeur'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\nimport { miseEnEvidence } from '../../lib/outils/embellissements'\n\nexport const titre = 'Calculate the volume of given solids'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\nexport const interactifReady = true\nexport const interactifType = ['qcm', 'mathLive']\nexport const dateDeModifImportante = '05/11/2023'\n/**\n * Calcul de volumes.\n * @author Jean-Claude Lhote (AMC par EE) // modifié par Mireille Gain pour y ajouter les décimaux\n * référence 6M30\n */\n\nexport const uuid = '04b0d'\nexport const ref = '6M30'\nexport default function CalculDeVolumes () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.nbQuestions = 4\n this.nbCols = 1\n this.nbColsCorr = 1\n this.sup = 1\n this.classe = 6\n this.amcReady = amcReady\n this.amcType = amcType\n this.interactifReady = interactifReady\n this.interactifType = interactifType\n this.sup3 = 2\n\n this.sup4 = 3\n let thissup4Max\n\n this.nouvelleVersion = function () {\n this.interactifType = this.sup3 === 2 ? 'mathLive' : 'qcm'\n let piApprox = false\n if (this.sup === 3) {\n this.sup = 1\n piApprox = true // calcul en prenant Pi environ 3\n }\n this.autoCorrection = []\n switch (this.classe) {\n case 6 :\n thissup4Max = 2\n break\n case 5 :\n thissup4Max = 4\n break\n case 4 :\n thissup4Max = 6\n break\n case 3 :\n thissup4Max = 7\n break\n }\n\n const typesDeQuestionsDisponibles = gestionnaireFormulaireTexte({\n min: 1,\n max: thissup4Max,\n defaut: thissup4Max + 1,\n melange: thissup4Max + 1,\n nbQuestions: Math.max(this.nbQuestions, thissup4Max),\n saisie: this.sup4,\n shuffle: true\n })\n\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions) // Tous les types de questions sont posées mais l'ordre diffère à chaque 'cycle'\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n const listeUnites = [\n [sp(1) + '\\\\text{m}', sp(1) + '\\\\text{m}^3', 'm^3'],\n [sp(1) + '\\\\text{dm}', sp(1) + '\\\\text{dm}^3', 'dm^3'],\n [sp(1) + '\\\\text{cm}', sp(1) + '\\\\text{cm}^3', 'cm^3'],\n [sp(1) + '\\\\text{mm}', sp(1) + '\\\\text{mm}^3', 'mm^3']\n ]\n let partieDecimale1, partieDecimale2, partieDecimale3\n if (this.sup2) {\n partieDecimale1 = new Decimal(randint(1, 9)).div(10).mul(randint(0, 1))\n partieDecimale2 = new Decimal(randint(1, 9)).div(10).mul(randint(0, 1))\n partieDecimale3 = new Decimal(randint(1, 9)).div(10).mul(randint(0, 1))\n } else {\n partieDecimale1 = new Decimal(0)\n partieDecimale2 = new Decimal(0)\n partieDecimale3 = new Decimal(0)\n }\n for (let i = 0, texte, texteCorr, L, l, h, c, r, j, resultat, resultat2, resultat3, resultat4, volume, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n this.autoCorrection[i] = {}\n texte = 'Calculate volume'\n switch (listeTypeDeQuestions[i]) {\n case 1: // cube\n c = new Decimal(randint(2, 10)).plus(partieDecimale1)\n volume = c.pow(3)\n j = randint(0, 3) // pour le choix de l'unité\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n texte += ` of a cube of $${texNombre(c, 1)} ${listeUnites[j][0]}$ of edge.`\n texteCorr = `$\\\\mathcal{V}= c^3 =c \\\\times c \\\\times c = ${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=`\n if (!volume.eq(volume.round())) {\n texteCorr += `${texNombre(volume)}${listeUnites[j][1]}\\\\approx ${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `${miseEnEvidence(`${texNombre(volume)}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n if (!c.eq(6)) resultat2 = c.pow(2).mul(6).round()\n else resultat2 = c.mul(24).round()\n if (!c.eq(2)) resultat3 = c.mul(4).round()\n else resultat3 = new Decimal(24)\n resultat4 = c.mul(6).round()\n break\n case 2: // pavé droit\n if (this.sup === 1) { // sans conversion\n j = randint(0, 3) // pour le choix de l'unité\n l = partieDecimale1.plus(randint(2, 5))\n h = partieDecimale2.plus(randint(3, 6))\n L = partieDecimale3.plus(randint(6, 10))\n volume = l.mul(L).mul(h)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n texte += ` a right block of $${texNombre(l, 1)}${listeUnites[j][0]}$ width, $${texNombre(L, 1)}${listeUnites[j][0]}$ length and $${texNombre(h)}${listeUnites[j][0]}$ height.`\n texteCorr = `$\\\\mathcal{V}= l \\\\times L \\\\times h = ${texNombre(l, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(L, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(h)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=`\n if (!volume.eq(volume.round())) {\n texteCorr += `${texNombre(volume)}${listeUnites[j][1]}\\\\approx ${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `${miseEnEvidence(`${texNombre(volume)}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n resultat2 = l.plus(L).plus(h).mul(6).round()\n if (resultat2.eq(resultat)) resultat2 = resultat2.div(2).round()\n resultat3 = l.mul(2).mul(L).plus(L.mul(h).mul(2)).plus(l.mul(h).mul(2)).round()\n resultat4 = l.plus(L).plus(h).mul(2).round()\n } else {\n // with conversion\n j = randint(1, 2) // pour le choix de l'unité centrale\n l = partieDecimale1.plus(randint(2, 5))\n h = partieDecimale2.plus(randint(3, 6)).mul(10)\n L = new Decimal(randint(6, 10)).div(10)\n volume = l.mul(L).mul(h)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, `\n texte += ` a right block of $${texNombre(l, 1)}${listeUnites[j][0]}$ width, $${texNombre(L, 1)}${listeUnites[j - 1][0]}$ length and $${texNombre(h)}${listeUnites[j + 1][0]}$ height.`\n texteCorr = `$\\\\mathcal{V}= l \\\\times L \\\\times h = ${texNombre(l, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(L, 1)}${listeUnites[j - 1][0]}\\\\times${texNombre(h, 0)}${listeUnites[j + 1][0]}=${texNombre(l, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(L * 10)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(h.div(10), 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=`\n if (!volume.eq(volume.round())) {\n texteCorr += `${texNombre(volume)}${listeUnites[j][1]}\\\\approx ${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `${miseEnEvidence(`${texNombre(volume)}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n resultat2 = l.plus(L).plus(h).mul(6).round()\n resultat3 = l.mul(2).mul(L).plus(L.mul(h).mul(2)).plus(l.mul(h).mul(2)).round()\n resultat4 = l.plus(L).plus(h).mul(2).round()\n }\n break\n case 3: // Cylindre\n if (this.sup === 1) {\n // without conversion\n j = randint(0, 3) // pour le choix de l'unité\n r = new Decimal(randint(2, 10))\n h = new Decimal(randint(2, 15))\n\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n if (piApprox) {\n volume = r.pow(2).mul(h).mul(3)\n texte += ', taking $\\\\pi \\\\approx 3$,' // On prend pi = 3\n } else {\n volume = r.pow(2).mul(h).mul(Decimal.acos(-1))\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, ` // Il faut toujours arrondir à cause de la présence de Pi\n }\n let diametre = choice([true, false])\n\n diametre = true\n if (diametre) {\n texte += `of a cylinder of $${2 * r}${listeUnites[j][0]}$ in diameter and $${texNombre(h, 0)}${listeUnites[j][0]}$ in height.`\n } else {\n texte += `of a cylinder of $${r}${listeUnites[j][0]}$ radius and $${texNombre(h, 0)}${listeUnites[j][0]}$ height.`\n }\n if (piApprox) {\n texteCorr = (diametre ? `$R = diameter \\\\div 2 = ${2 * r}${listeUnites[j][0]} \\\\div 2 = ${r}${listeUnites[j][0]}$<br>` : '')\n texteCorr += `$\\\\mathcal{V}=\\\\pi \\\\times R ^2 \\\\times h =\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h, 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${texNombre(\n r.pow(2).mul(h), 0)}\\\\pi${listeUnites[j][1]}\\\\approx ${texNombre(\n r.pow(2).mul(h), 0)}\\\\times 3${listeUnites[j][1]} \\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr = (diametre ? `$R = diameter \\\\div 2 = ${2 * r}${listeUnites[j][0]} \\\\div 2 = ${r}${listeUnites[j][0]}$<br>` : '')\n texteCorr += `$\\\\mathcal{V}=\\\\pi \\\\times R ^2 \\\\times h =\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h, 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${texNombre(\n r.pow(2).mul(h), 0)}\\\\pi${listeUnites[j][1]}\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n } else {\n j = randint(2, 3) // pour le choix de l'unité\n r = new Decimal(randint(2, 10))\n h = new Decimal(randint(20, 150))\n volume = r.pow(2).mul(h).mul(Decimal.acos(-1))\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, `\n texte += ` of a cylinder of $${r}${listeUnites[j][0]}$ radius and $${texNombre(h.div(10), 1)}${listeUnites[j - 1][0]}$ height.`\n texteCorr = `$\\\\mathcal{V}=\\\\pi \\\\times R ^2 \\\\times h =\\\\pi\\\\times\\\\left(${texNombre(r, 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h.div(10), 1)}${listeUnites[j - 1][0]}=\\\\pi\\\\times${texNombre(r.mul(r), 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}^ 2\\\\times${texNombre(h, 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${texNombre(r.pow(2).mul(h), 0)}\\\\pi${listeUnites[j][1]}\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n resultat2 = volume.mul(4).round()\n resultat3 = volume.div(2).round()\n resultat4 = volume.mul(2).round()\n break\n case 4: // prisme droit\n if (this.sup === 1) {\n // without conversion\n j = randint(0, 3) // pour le choix de l'unité\n c = partieDecimale3.plus(randint(2, 10))\n h = randint(2, 5)\n l = randint(6, 10)\n volume = c.mul(h * l).div(2)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n if (choice([false, true])) {\n texte += ` of a right prism of height $${l}${listeUnites[j][0]}$. The base of the right prism is a right triangle whose sides of the right angle measure $${texNombre(c, 1)}${listeUnites[j][0]}$ and $${h}${listeUnites[j][0]}$.`\n } else {\n texte += ` of a right prism of height $${l}${listeUnites[j][0]}$ and whose bases are triangles of base $${texNombre(c, 1)}${listeUnites[j][0]}$ and of corresponding height $${h}${listeUnites[j][0]}$.`\n }\n texteCorr = `$\\\\mathcal{V}=\\\\mathcal{B} \\\\times h=\\\\dfrac{${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${h}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}}{2}\\\\times${l}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=`\n } else {\n j = randint(1, 2) // pour le choix de l'unité\n c = partieDecimale3.plus(randint(2, 10))\n h = new Decimal(randint(30, 50))\n l = new Decimal(randint(5, 15)).div(10)\n volume = c.mul(h).mul(l).div(2)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n texte += ` of a right prism of height $${texNombre(l, 1)}${listeUnites[j - 1][0]}$ and whose bases are triangles of base $${texNombre(c, 1)}${listeUnites[j][0]}$ and of corresponding height $${h}${listeUnites[j + 1][0]}$.`\n texteCorr = `$\\\\mathcal{V}=\\\\mathcal{B} \\\\times h=\\\\dfrac{${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${h}${listeUnites[j + 1][0]}}{2}\\\\times${texNombre(l, 1)}${listeUnites[j - 1][0]}=\\\\dfrac{${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\times${texNombre(h.div(10), 1)\n }${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}}{2}\\\\times${texNombre(l.mul(10), 0)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=`\n }\n if (!volume.eq(volume.round())) {\n texteCorr += `${texNombre(volume, 2)}${listeUnites[j][1]}\\\\approx ${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `${miseEnEvidence(`${texNombre(volume, 2)}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n resultat2 = volume.mul(4).round()\n resultat3 = c.plus(h).mul(l).round()\n resultat4 = volume.mul(2).round()\n break\n case 5: // cone\n if (this.sup === 1) {\n // without conversion\n j = randint(0, 3) // pour le choix de l'unité\n r = randint(2, 10)\n h = randint(2, 15)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n if (piApprox) {\n volume = new Decimal(r * r * h).mul(3).div(3)\n texte += ', taking $\\\\pi \\\\approx 3$,' // On prend pi = 3\n } else {\n volume = new Decimal(r * r * h).mul(Decimal.acos(-1)).div(3)\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, ` // Il faut toujours arrondir à cause de la présence de Pi\n }\n const diametre = randint(0, 1)\n if (diametre) {\n // diameter\n texte += `of a cone of $${2 * r}${listeUnites[j][0]}$ in diameter and $${h}${listeUnites[j][0]}$ in height.`\n } else {\n texte += `of a cone of $${r}${listeUnites[j][0]}$ radius and $${h}${listeUnites[j][0]}$ height.`\n }\n if (piApprox) {\n texteCorr = (diametre ? `$R = diameter \\\\div 2 = ${2 * r}${listeUnites[j][0]} \\\\div 2 = ${r}${listeUnites[j][0]}$<br>` : '')\n texteCorr += `$\\\\mathcal{V}=\\\\dfrac{1}{3} \\\\times \\\\mathcal{B} \\\\times h=\\\\dfrac{1}{3}\\\\times\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${h}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${deprecatedTexFraction(\n r * r * h, 3)}\\\\pi${listeUnites[j][1]}\\\\approx${deprecatedTexFraction(\n r * r * h, 3)}\\\\times 3 \\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr = (diametre ? `$R = diameter \\\\div 2 = ${2 * r}${listeUnites[j][0]} \\\\div 2 = ${r}${listeUnites[j][0]}$<br>` : '')\n texteCorr += `$\\\\mathcal{V}=\\\\dfrac{1}{3} \\\\times \\\\mathcal{B} \\\\times h=\\\\dfrac{1}{3}\\\\times\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${h}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${deprecatedTexFraction(\n r * r * h, 3)}\\\\pi${listeUnites[j][1]}\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n } else {\n j = randint(2, 3) // pour le choix de l'unité\n r = randint(2, 10)\n h = randint(20, 150)\n volume = new Decimal(r * r * h).mul(Decimal.acos(-1)).div(3)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, ` // Il faut toujours arrondir à cause de la présence de Pi\n texte += `of a cone of $${r}${listeUnites[j][0]}$ radius and $${texNombre(h / 10, 1)}${listeUnites[j - 1][0]}$ height.`\n texteCorr = `$\\\\mathcal{V}=\\\\dfrac{1}{3} \\\\times \\\\mathcal{B} \\\\times h=\\\\dfrac{1}{3}\\\\times\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h / 10, 1)}${listeUnites[j - 1][0]}=\\\\dfrac{1}{3}\\\\times\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}=${deprecatedTexFraction(r * r * h, 3)}\\\\pi\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n resultat = volume.round()\n resultat2 = volume.mul(4).round()\n resultat3 = volume.div(2).round()\n resultat4 = volume.mul(2).round()\n break\n case 6: // pyramide\n if (this.sup === 1) {\n // without conversion\n j = randint(0, 3) // pour le choix de l'unité\n c = partieDecimale2.plus(randint(2, 10))\n h = randint(2, 5)\n l = randint(6, 10)\n volume = c.mul(c).mul(h).div(3)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n texte += ` of a pyramid of height $${h}${listeUnites[j][0]}$ and whose base is a square of side $${texNombre(c, 1)}${listeUnites[j][0]}$.`\n texteCorr = `$\\\\mathcal{V}=\\\\dfrac{1}{3} \\\\times \\\\mathcal{B} \\\\times h=\\\\dfrac{1}{3}\\\\times\\\\left(${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${h}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}`\n if (volume.eq(volume.round())) {\n texteCorr += `=${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n } else {\n j = randint(1, 2) // pour le choix de l'unité\n c = partieDecimale2.plus(randint(2, 10))\n h = randint(30, 50)\n l = new Decimal(randint(5, 15)).div(10)\n volume = c.mul(c).mul(h).div(3)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += !volume.eq(volume.round()) ? `, rounded to the nearest $${listeUnites[j][1]}$, ` : ''\n texte += ` of a pyramid of height $${texNombre(h / 10, 1)}${listeUnites[j - 1][0]}$ and whose base is a square of side $${texNombre(c, 1)}${listeUnites[j][0]}$.`\n texteCorr = `$\\\\mathcal{V}=\\\\dfrac{1}{3} \\\\times \\\\mathcal{B} \\\\times h=\\\\dfrac{1}{3}\\\\times\\\\left(${texNombre(c, 1)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^2\\\\times${texNombre(h / 10, 1)}${listeUnites[j - 1][0]}=\\\\dfrac{1}{3}\\\\times${texNombre(c.mul(c), 2)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}^2\\\\times${texNombre(h)}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}`\n if (volume.eq(volume.round())) {\n texteCorr += `=${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n } else {\n texteCorr += `\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n }\n }\n resultat = volume.round()\n resultat2 = volume.mul(3).round()\n resultat3 = volume.mul(3).div(4).round()\n resultat4 = volume.div(2).round()\n break\n case 7: // boule\n j = randint(0, 3) // pour le choix de l'unité\n r = randint(2, 10)\n volume = new Decimal(r).pow(3).mul(4).mul(Decimal.acos(-1)).div(3)\n texte += context.isAmc ? ` in$${listeUnites[j][1]}$` : ''\n texte += `, rounded to the nearest $${listeUnites[j][1]}$, `\n texte += ` of a ball of radius $${r}${listeUnites[j][0]}$.`\n texteCorr = `$\\\\mathcal{V}=\\\\dfrac{4}{3} \\\\times \\\\pi \\\\times R^3=\\\\dfrac{4}{3}\\\\times\\\\pi\\\\times\\\\left(${r}${context.isAmc ? listeUnites[j][2] : listeUnites[j][0]}\\\\right)^3=${deprecatedTexFraction(4 * r * r * r, 3)}\\\\pi${listeUnites[j][1]}\\\\approx${miseEnEvidence(`${texNombre(volume.round())}${listeUnites[j][1]}`)}$`\n resultat = volume.round()\n resultat2 = volume.mul(3).round()\n resultat3 = volume.mul(3).div(4).round()\n resultat4 = volume.div(2).round()\n break\n }\n this.autoCorrection[i].enonce = `${texte}\\n`\n this.autoCorrection[i].propositions = [{\n texte: `$${texNombre(resultat)} ${listeUnites[j][1]}$`,\n statut: true\n },\n {\n texte: `$${texNombre(resultat2)} ${listeUnites[j][1]}$`,\n statut: false\n },\n {\n texte: `$${texNombre(resultat3)} ${listeUnites[j][1]}$`,\n statut: false\n },\n {\n texte: `$${texNombre(resultat4)} ${listeUnites[j][1]}$`,\n statut: false\n }\n ]\n resultat = resultat.toNumber()\n resultat2 = resultat2.toNumber()\n resultat3 = resultat3.toNumber()\n resultat4 = resultat4.toNumber()\n if (this.interactif && this.interactifType === 'qcm') {\n texte += propositionsQcm(this, i).texte\n } else {\n setReponse(this, i, new Grandeur(resultat, listeUnites[j][2]), { formatInteractif: 'units' })\n texte += ajouteChampTexteMathLive(this, i, 'units[volumes]', { texteAvant: '<br>' + sp(12) + 'You should remember to indicate the unit for the response volume:' })\n }\n if (context.isAmc) {\n if (this.sup3 === 1) {\n this.autoCorrection[i] = {\n enonce: '',\n enonceAvant: false,\n propositions: [\n {\n type: 'qcmMono',\n enonce: texte,\n propositions: [\n {\n texte: `$${texNombre(resultat)} ${listeUnites[j][1]}$`,\n statut: true\n },\n {\n texte: `$${texNombre(resultat2)} ${listeUnites[j][1]}$`,\n statut: false\n },\n {\n texte: `$${texNombre(resultat3)} ${listeUnites[j][1]}$`,\n statut: false\n },\n {\n texte: `$${texNombre(resultat4)} ${listeUnites[j][1]}$`,\n statut: false\n }\n ],\n options: {\n ordered: false // (si les réponses doivent rester dans l'order above, false s'il faut les mélanger),\n }\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte + '\\\\\\\\Write the calculation:',\n enonceAvant: true,\n options: {\n multicols: true,\n barreseparation: false,\n multicolsAll: false,\n numerotationEnonce: true\n },\n propositions: [\n {\n type: 'AMCOpen',\n propositions: [{\n texte: texteCorr,\n numQuestionVisible: false,\n enonce: '',\n statut: 6\n }\n ]\n },\n {\n type: 'AMCNum',\n propositions: [{\n texte: '',\n statut: '',\n reponse: {\n texte: '',\n valeur: [resultat],\n param: {\n digits: nombreDeChiffresDansLaPartieEntiere(resultat) + randint(0, 2),\n decimals: 0,\n signe: false,\n approx: 0\n }\n }\n }]\n }\n ]\n }\n }\n }\n if (this.questionJamaisPosee(i, resultat, resultat2, resultat3, resultat4)) {\n // If the question has never been asked, we create another one\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n if (this.sup === 1 && piApprox) {\n this.sup = 3\n }\n }\n this.besoinFormulaireNumerique = [\n 'Difficulty level',\n 2,\n '1: Without conversion\\n2: With conversions'\n ]\n this.besoinFormulaire2CaseACocher = ['With decimals', false]\n this.besoinFormulaire3Numerique = ['Type of interactive exercise or AMC', 2, '1: QCM\\n2: Numerical'] // Texte, tooltip\n this.besoinFormulaire4Texte = ['Type of solids', 'Numbers separated by hyphens\\n1: Cubes\\n2: Right tiles\\n3: 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