197:@0.942817:0.963099:0.970993:0.963099:0.970993:0.946475:0.942817:0.946475:0.000000:0.000000:0.000000
M.3.2.11. Reconocer los elementos de un círculo en representaciones gráficas, y calcular la longitud (perímetro) de la circunferencia y el área de un círculo en la :@0.105857:0.082619:0.877642:0.082619:0.877642:0.072040:0.105857:0.072040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolución de problemas.:@0.105857:0.093180:0.228681:0.093180:0.228681:0.082601:0.105857:0.082601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Perímetro de la circunferencia :@0.096359:0.167786:0.381474:0.167786:0.381474:0.147812:0.096359:0.147812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Daniel desea saber cuántos metros recorre la llanta de su bicicleta al dar :@0.096359:0.192704:0.699098:0.192704:0.699098:0.174825:0.096359:0.174825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tres vueltas completas, si el radio de la llanta mide 40 cm.:@0.096359:0.210809:0.552248:0.210809:0.552248:0.192930:0.096359:0.192930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para saber cuántos metros recorre la llanta de la bicicleta, observemos los :@0.096359:0.236036:0.699102:0.236036:0.699102:0.218157:0.096359:0.218157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
datos::@0.096359:0.254141:0.144204:0.254141:0.144204:0.236262:0.096359:0.236262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diámetro = 2 × r :@0.096359:0.279367:0.231169:0.279367:0.231169:0.261488:0.096359:0.261488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.277285:0.279367:0.281687:0.279367:0.281687:0.261488:0.277285:0.261488:0.000000
d = 80 cm:@0.337593:0.279367:0.418769:0.279367:0.418769:0.261488:0.337593:0.261488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.307113:0.100761:0.307113:0.100761:0.289235:0.096359:0.289235:0.000000
π:@0.129175:0.304096:0.140211:0.304096:0.145191:0.287107:0.134155:0.287107:0.000000
=:@0.115629:0.304096:0.126666:0.304096:0.126666:0.287107:0.115629:0.287107:0.000000
×:@0.146829:0.304096:0.157866:0.304096:0.157866:0.287107:0.146829:0.287107:0.000000
L:@0.103266:0.303357:0.111589:0.303357:0.111589:0.285508:0.103266:0.285508:0.000000
d:@0.161484:0.303357:0.171596:0.303357:0.171596:0.285508:0.161484:0.285508:0.000000
=:@0.111227:0.331843:0.122263:0.331843:0.122263:0.314855:0.111227:0.314855:0.000000
×:@0.163052:0.331843:0.174089:0.331843:0.174089:0.314855:0.163052:0.314855:0.000000
L:@0.098864:0.331104:0.107186:0.331104:0.107186:0.313255:0.098864:0.313255:0.000000
3,14 80:@0.126505:0.331104:0.196724:0.331104:0.196724:0.313225:0.126505:0.313225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    :@0.200224:0.336133:0.221378:0.336133:0.221378:0.318254:0.200224:0.318254:0.000000:0.000000:0.000000:0.000000
 :@0.277284:0.336133:0.281687:0.336133:0.281687:0.318254:0.277284:0.318254:0.000000
L = 251,2 cm:@0.337587:0.336133:0.439951:0.336133:0.439951:0.318254:0.337587:0.318254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
251,2 cm a m = 251, 2 ÷ 100 = 2,512 m:@0.096352:0.361360:0.405856:0.361360:0.405856:0.343481:0.096352:0.343481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,512 m × 3 = 7,536 m:@0.096352:0.386586:0.274946:0.386586:0.274946:0.368707:0.096352:0.368707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al dar 3 vueltas, la rueda de la bicicleta ha recorrido 7,536 m.:@0.096352:0.411813:0.577247:0.411813:0.577247:0.393934:0.096352:0.393934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.255422:0.501664:0.264619:0.501664:0.268769:0.487507:0.259572:0.487507:0.000000
=×:@0.244326:0.501664:0.279020:0.501664:0.279020:0.487507:0.244326:0.487507:0.000000:0.000000
L:@0.234174:0.501048:0.241110:0.501048:0.241110:0.486174:0.234174:0.486174:0.000000
d:@0.281718:0.501048:0.290144:0.501048:0.290144:0.486174:0.281718:0.486174:0.000000
π:@0.440838:0.504931:0.451874:0.504931:0.456854:0.487942:0.445818:0.487942:0.000000
=:@0.427293:0.504931:0.438329:0.504931:0.438329:0.487942:0.427293:0.487942:0.000000
×:@0.458492:0.504931:0.469529:0.504931:0.469529:0.487942:0.458492:0.487942:0.000000
L:@0.414929:0.504192:0.423252:0.504192:0.423252:0.486343:0.414929:0.486343:0.000000
r:@0.482676:0.504192:0.488445:0.504192:0.488445:0.486343:0.482676:0.486343:0.000000
2:@0.472725:0.504192:0.482535:0.504192:0.482535:0.486313:0.472725:0.486313:0.000000
Área del círculo:@0.096359:0.572410:0.241421:0.572410:0.241421:0.552437:0.096359:0.552437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Carla desea colocar un espejo circular en un marco que tiene de diámetro :@0.096359:0.597329:0.699059:0.597329:0.699059:0.579450:0.096359:0.579450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
60 cm. ¿Cuántos centímetros cuadrados de espejo necesita comprar?:@0.096359:0.615434:0.650008:0.615434:0.650008:0.597555:0.096359:0.597555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para saber cuántos centímetros de espejo necesita comprar, debemos :@0.096359:0.665902:0.699084:0.665902:0.699084:0.648023:0.096359:0.648023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontrar el área del círculo.:@0.096359:0.684007:0.321409:0.684007:0.321409:0.666128:0.096359:0.666128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.136080:0.723808:0.147116:0.723808:0.152096:0.706819:0.141060:0.706819:0.000000
=:@0.122535:0.723808:0.133571:0.723808:0.133571:0.706819:0.122535:0.706819:0.000000
×:@0.153734:0.723808:0.164771:0.723808:0.164771:0.706819:0.153734:0.706819:0.000000
A:@0.100542:0.723069:0.111337:0.723069:0.111337:0.705220:0.100542:0.705220:0.000000
r:@0.168389:0.723069:0.174159:0.723069:0.174159:0.705220:0.168389:0.705220:0.000000
o:@0.110075:0.725249:0.115886:0.725249:0.115886:0.714931:0.110075:0.714931:0.000000
2:@0.175775:0.714720:0.181447:0.714720:0.181447:0.704383:0.175775:0.704383:0.000000
   :@0.185147:0.741928:0.198354:0.741928:0.198354:0.724049:0.185147:0.724049:0.000000:0.000000:0.000000
=:@0.224530:0.710921:0.235566:0.710921:0.235566:0.693932:0.224530:0.693932:0.000000
×:@0.276355:0.710921:0.287392:0.710921:0.287392:0.693932:0.276355:0.693932:0.000000
=:@0.224530:0.735514:0.235566:0.735514:0.235566:0.718525:0.224530:0.718525:0.000000
×:@0.276355:0.735514:0.287392:0.735514:0.287392:0.718525:0.276355:0.718525:0.000000
=:@0.323898:0.735514:0.334935:0.735514:0.334935:0.718525:0.323898:0.718525:0.000000
A:@0.202557:0.710181:0.213353:0.710181:0.213353:0.692333:0.202557:0.692333:0.000000
A:@0.202542:0.734778:0.213338:0.734778:0.213338:0.716929:0.202542:0.716929:0.000000
cm:@0.392796:0.734778:0.416705:0.734778:0.416705:0.716929:0.392796:0.716929:0.000000:0.000000
3,14 30:@0.239820:0.710185:0.310039:0.710185:0.310039:0.692306:0.239820:0.692306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3,14 900 2 826:@0.239820:0.734778:0.384219:0.734778:0.384219:0.716899:0.239820:0.716899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o:@0.212069:0.712362:0.217881:0.712362:0.217881:0.702043:0.212069:0.702043:0.000000
o:@0.212069:0.736960:0.217881:0.736960:0.217881:0.726641:0.212069:0.726641:0.000000
2:@0.310542:0.701834:0.316214:0.701834:0.316214:0.691498:0.310542:0.691498:0.000000
2:@0.416918:0.726432:0.422590:0.726432:0.422590:0.716095:0.416918:0.716095:0.000000
π:@0.422335:0.835026:0.433371:0.835026:0.438351:0.818038:0.427315:0.818038:0.000000
=:@0.408789:0.835026:0.419826:0.835026:0.419826:0.818038:0.408789:0.818038:0.000000
×:@0.439989:0.835026:0.451026:0.835026:0.451026:0.818038:0.439989:0.818038:0.000000
A:@0.386797:0.834287:0.397592:0.834287:0.397592:0.816438:0.386797:0.816438:0.000000
r:@0.454644:0.834287:0.460414:0.834287:0.460414:0.816438:0.454644:0.816438:0.000000
o:@0.396329:0.836468:0.402140:0.836468:0.402140:0.826149:0.396329:0.826149:0.000000
2:@0.462030:0.825938:0.467702:0.825938:0.467702:0.815602:0.462030:0.815602:0.000000
Shutterstock, (2020). 144125206:@0.923014:0.278863:0.923014:0.183208:0.911103:0.183208:0.911103:0.278863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El diámetro de una :@0.733188:0.461354:0.875761:0.461354:0.875761:0.444965:0.733188:0.444965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
circunferencia mide el :@0.733188:0.477701:0.899203:0.477701:0.899203:0.461313:0.733188:0.461313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
doble que el radio. :@0.733188:0.494049:0.874084:0.494049:0.874084:0.477660:0.733188:0.477660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Diámetro = 2 radios:@0.733188:0.510396:0.878525:0.510396:0.878525:0.494007:0.733188:0.494007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D = 2r:@0.733188:0.530312:0.777728:0.530312:0.777728:0.513674:0.733188:0.513674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.783165:0.422952:0.884276:0.422952:0.884276:0.406176:0.783165:0.406176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.783165:0.436783:0.871194:0.436783:0.871194:0.420006:0.783165:0.420006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pixabay.com:@0.926589:0.840553:0.926589:0.803212:0.914678:0.803212:0.914678:0.840553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000