import{E as $e,c as d,h as Q,r as w,cj as ne,b4 as c,K as fe,q as b,C as W,n as m,R as j,U as M,o as R,aa as G,w as e,cD as p,ci as le,l as me}from"./index-ajJ0B2-K.js";import{c as C}from"./lists-u4BnmFNs.js";import{b as D}from"./style-YtQgMMZt.js";import{a as h,b as he,e as ue,g as de}from"./3d-a5FjzFK6.js";import"./aleatoires-mDu76THU.js";import"./dateEtHoraires-L3F4WBTY.js";const be="Arithmetic & volumes",ke="2e22a",we="3A14-0";function Ce(){$e.call(this),this.titre=be,this.introduction="According to Brevet des Collèges - Foreign centers - June 2022",this.consigne="",d.isHtml?this.spacing=1:this.spacing=2,d.isHtml?this.spacingCorr=2:this.spacingCorr=2,this.nbQuestions=1,this.nbQuestionsModifiable=!1,this.nbCols=1,this.nbColsCorr=1,this.nouvelleVersion=function(){d.anglePerspective=50;const E=Q([2,3,5,7]),J=Q([2,3,5,7]),$=E*J,x=w(5,12),P=ne(x),n=P+x,s=$*x,r=$*P,O=s+r;let a="To celebrate the 25th anniversary of his shop, a chocolatier wants to offer the first customers of the day a box containing chocolate truffles.<br><br>";a+=`${D("1.")} He made $${O}$ truffles: $${s}$ coffee flavored truffles and $${r}$ coconut coated truffles. He wants to make these boxes so that:`,d.isHtml?a+=C({items:["The number of coffee flavored truffles is the same in each box;","The number of coconut-coated truffles is the same in each box;","All truffles are used."],style:"arrows",classOptions:'style="color: red; backgroundColor: red"'}).outerHTML:a+=C({items:["The number of coffee flavored truffles is the same in each box;","The number of coconut-coated truffles is the same in each box;","All truffles are used."],style:"arrows",classOptions:'style="color: red; backgroundColor: red"'}),d.isHtml?(a+=`${c(0)} Decompose $${s}$ and $${r}$ into product of prime factors.<br>`,a+=`${c(1)} Deduce the list of divisors common to $${s}$ and $${r}$.<br>`,a+=`${c(2)} What maximum number of boxes can he make?<br>`,a+=`${c(3)} In this case, how many truffles of each type will there be in each box?<br><br>`):(a+=`${c(0)} Decompose $${s}$ and $${r}$ into product of prime factors.<br>`,a+=`${c(1)} Deduce the list of divisors common to $${s}$ and $${r}$.<br>`,a+=`${c(2)} What maximum number of boxes can he make?<br>`,a+=`${c(3)} In this case, how many truffles of each type will there be in each box?<br><br>`);const t=30,o=20,K=fe([b(0,0),b(t,0),b(t,o),b(0,o)]),U=W(b(0,o/3),b(t,o/3)),V=W(b(t/2,o),b(t/2,0)),A=m("type A",t/4-1,o-1,"medium","black",2),H=m("type B",3*t/4-1,o-1,"medium","black",2);A.epaisseur=4,A.contour=!0,A.couleurDeRemplissage=j("black"),H.epaisseur=4,H.contour=!0,H.couleurDeRemplissage=j("black");const z=h(t/4-2,4,o-4),S=he([h(t/4-6,0,o/3+1),h(t/4+2,0,o/3+1),h(t/4+2,8,o/3+1),h(t/4-6,8,o/3+1)]),X=ue(S,z),Y=[h(3*t/4-5,0,o/3+2),h(3*t/4+3,0,o/3+2),h(3*t/4-5,0,o-5),h(3*t/4-5,5,o/3+2)],Z=de(...Y),f=w(10,15)/10,u=n*4*Math.PI*(f/2)**3/3,q=1.7*u,F=2.3*u;let l,g;const v=w(4,5),y=w(2,3)-.5,T=w(4,6),L=Math.random()<.5;L?(g=Number((q/v/y).toFixed(1)),l=Number(Math.sqrt(3*F/T).toFixed(1))):(g=Math.round(F/v/y),l=Number(Math.sqrt(3*q/T).toFixed(1)));const B=y*v*g,k=T*l**2/3,_=m("Pyramid with square base",t/4,o/3-1,"medium","black",1.5),ee=m(`side ${M(l,1).replace(",",".")} cm`,t/4,o/3-2,"medium","black",1.5),te=m(`and height ${M(T,1).replace(",",".")} cm`,t/4,o/3-3,"medium","black",1.5),oe=m("Right pad",3*t/4,o/3-1,"medium","black",1.5),se=m(`length ${v} cm`,3*t/4,o/3-2,"medium","black",1.5),re=m(`width ${M(y,1).replace(",",".")} cm`,3*t/4,o/3-3,"medium","black",1.5),ae=m(`and height ${M(g,1).replace(",",".")} cm`,3*t/4,o/3-4,"medium","black",1.5),I=[K,U,V,A,H,X.c2d,Z.c2d,_,ee,te,oe,se,re,ae];a+=`${D("2.")} The chocolatier wants to make boxes containing $${n}$ truffles. For this, he has the choice between two types of boxes which can contain the $${n}$ truffles, and whose characteristics are given below:`,a+="<br>"+R(Object.assign({scale:.5},G(I)),I),a+=`In this question, each of the $${n}$ truffles is compared to a ball of diameter $${e(f,1)}$ cm.<br>`,a+="Inside a box, so that the truffles are not damaged during transport, the volume occupied by the truffles must be greater than the volume not occupied by the truffles.<br>",a+="What type(s) of box should the chocolatier choose for this condition to be met?",this.listeQuestions[0]=a;let i=R(Object.assign({scale:.5},G(I)),I);i+=`${D("1.")} He made $${O}$ truffles: $${s}$ coffee flavored truffles and $${r}$ coconut coated truffles. He wants to make these boxes so that:`,d.isHtml?i+=C({items:["The number of coffee flavored truffles is the same in each box;","The number of coconut-coated truffles is the same in each box;","All truffles are used."],style:"arrows",classOptions:'style="backGroundColor: red";'}).outerHTML:i+=C({items:["The number of coffee flavored truffles is the same in each box;","The number of coconut-coated truffles is the same in each box;","All truffles are used."],style:"arrows",classOptions:'style="backGroundColor: red";'}),d.isHtml?(i+=`${c(0)} $${s} = ${p(s)}$ and $${r} = ${p(r)}$.<br>`,i+=`${c(1)} We are looking for the greatest common divisor of $${s}$ and $${r}$.<br>`,i+=`In the prime factor decompositions of $${s}$ and $${r}$, we find $${p($)}$, so their greatest common divisor is $${p($)} = ${$}$.<br>`,i+=`${c(2)} The maximum number of boxes he can make is therefore $${$}$.<br>`,i+=`${c(3)} There will therefore be $\\dfrac{${s}}{${$}} = ${x}$ coffee truffles per box and $\\dfrac{${r}}{${$}} = ${P}$ coconut truffles per box.<br><br>`):(i+=`${c(0)} $${s} = ${p(s)}$ and $${r} = ${p(r)}$.<br>`,i+=`${c(1)} We are looking for the greatest common divisor of $${s}$ and $${r}$.<br>`,i+=`In the prime factor decompositions of $${s}$ and $${r}$, we find $${p($)}$, so their greatest common divisor is $${p($)} = ${$}$.<br>`,i+=`${c(2)} The maximum number of boxes he can make is therefore $${$}$.<br>`,i+=`${c(3)} There will therefore be $\\dfrac{${s}}{${$}} = ${x}$ coffee truffles per box and $\\dfrac{${r}}{${$}} = ${P}$ coconut truffles per box.<br><br>`),i+=`${D("2.")} In this question, each of the $${n}$ truffles is compared to a ball of diameter $${e(f,1)}$ cm.<br>`,i+="Inside a box, so that the truffles are not damaged during transport, the volume occupied by the truffles must be greater than the volume not occupied by the truffles.<br>";const ie={items:[`The pyramid has a square base of side $${e(l,1)}$ cm, the area of its base is therefore in cm$^2$: $${e(l,1)}\\times ${e(l,1)} = ${e(l**2,2)}$cm$^2$.`,`Its volume in cm$^3$ is: $\\dfrac{\\text{area of the base}\\times\\text{height}}{3}=\\dfrac{${e(l**2,2)}\\times ${T}}{3 }${le(k,1)}${e(k,1)}$ cm$^3$.`,`The volume of the pyramid is approximately $${e(k,1)}$ cm$^3$; that of truffles is approximately $${e(u,1)}$ cm$^3$.`,`The volume not occupied by the truffles is approximately $${e(k,1)}-${e(u,1)}$ or $${e(k-u,1)}$ cm$^3$`,L?"it is greater than the volume of the truffles, so the pyramid-shaped box is not suitable.":"it is less than the volume of the truffles, so the pyramid-shaped box is suitable."],style:"arrows",introduction:"The pyramid: "},ce={items:[`The right pad has a volume in cm$^3$ of: $${e(y,1)}\\times ${e(v,1)} \\times ${e(g,1)} = ${e(B,3)}$.`,`The volume of the right pad is $${e(B,1)}$ cm$^3$; that of truffles is approximately $${e(u,1)}$ cm$^3$.`,`The volume not occupied by the truffles is approximately $${e(B,1)}-${e(u,1)}$ or $${e(B-u,1)}$ cm$^3$.`,L?"it is less than the volume of the truffles, so the box shaped like a straight block is suitable.":"it is greater than the volume of the truffles, so the box shaped like a straight block is not suitable."],style:"arrows",introduction:"The right pad: "},N=C({items:[`A truffle is likened to a ball of diameter $${e(f,1)}$ cm, therefore of radius $${e(f/2,2)}$ cm and its volume in cm$^3$ is: $\\dfrac{4}{3}\\times\\pi\\ times${e(f/2,2)}^3$.`,`The volume occupied by $${n}$ truffles is therefore: $${n}\\times\\dfrac{4}{3}\\times\\pi\\times${e(f/2,2)}^3=\\dfrac{${e(n*4*(f/2)**3,4)}}{3}\\pi $ or approximately $${e(n*4*Math.PI*(f/2)**3/3,1)}$cm$^3$.`,ie,ce],style:"fleas"});i+=d.isHtml?N.outerHTML:N,this.listeCorrections[0]=i,me(this)}}export{Ce as default,we as ref,be as titre,ke as uuid};
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