218:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Geometría:@0.073089:0.043661:0.168070:0.043661:0.168070:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.293660:0.136887:0.369443:0.136887:0.369443:0.120217:0.293660:0.120217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calcular el volumen de los cuerpos geométricos.:@0.293660:0.160671:0.645627:0.160671:0.645627:0.144237:0.293660:0.144237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.:@0.322118:0.188033:0.333604:0.188033:0.333604:0.171599:0.322118:0.171599:0.000000:0.000000
 :@0.669687:0.188039:0.673405:0.188039:0.673405:0.170856:0.669687:0.170856:0.000000
b.:@0.673331:0.188039:0.686290:0.188039:0.686290:0.171605:0.673331:0.171605:0.000000:0.000000
 :@0.686290:0.188039:0.690193:0.188039:0.690193:0.171369:0.686290:0.171369:0.000000
Solución:@0.293663:0.355789:0.359797:0.355789:0.359797:0.339119:0.293663:0.339119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.:@0.325203:0.384580:0.336690:0.384580:0.336690:0.368146:0.325203:0.368146:0.000000:0.000000
Se trata de una pirámide cuadrangular. Reemplazamos los datos conocidos en:@0.355405:0.384580:0.926913:0.384580:0.926913:0.368146:0.355405:0.368146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la fórmula:@0.355331:0.409793:0.427953:0.409793:0.427953:0.393359:0.355331:0.393359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b. Es un prisma rectangular, por tanto, reemplazamos los datos en la fórmula:@0.325203:0.497847:0.890504:0.497847:0.890504:0.481413:0.325203:0.481413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.293660:0.599284:0.369443:0.599284:0.369443:0.582614:0.293660:0.582614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calcular el volumen del líquido depositado en el recipiente.:@0.293660:0.623073:0.723858:0.623073:0.723858:0.606639:0.293660:0.606639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De acuerdo con el gráfico, el radio de la :@0.293660:0.849124:0.593755:0.849124:0.593755:0.832691:0.293660:0.832691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esfera y de la base del cilindro es 30 cm y :@0.293660:0.865766:0.593879:0.865766:0.593879:0.849332:0.293660:0.849332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la altura del cilindro es 60 cm.:@0.293660:0.882408:0.507122:0.882408:0.507122:0.865974:0.293660:0.865974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.491926:0.189266:0.502404:0.189266:0.502404:0.172170:0.491926:0.172170:0.000000
 = 12 :@0.502007:0.189266:0.544634:0.189266:0.544634:0.172170:0.502007:0.172170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.544634:0.189266:0.568837:0.189266:0.568837:0.172170:0.544634:0.172170:0.000000:0.000000
4,5 :@0.374085:0.311758:0.401364:0.311758:0.401364:0.294661:0.374085:0.294661:0.000000:0.000000:0.000000:0.000000
cm:@0.401364:0.311758:0.425566:0.311758:0.425566:0.294661:0.401364:0.294661:0.000000:0.000000
4,5 :@0.493905:0.313535:0.521184:0.313535:0.521184:0.296439:0.493905:0.296439:0.000000:0.000000:0.000000:0.000000
cm:@0.521184:0.313535:0.545387:0.313535:0.545387:0.296439:0.521184:0.296439:0.000000:0.000000
10 :@0.743743:0.310567:0.767855:0.310567:0.767855:0.292928:0.743743:0.292928:0.000000:0.000000:0.000000
cm:@0.767855:0.310567:0.791831:0.310567:0.791831:0.292914:0.767855:0.292914:0.000000:0.000000
h:@0.833688:0.248964:0.844088:0.248964:0.844088:0.231311:0.833688:0.231311:0.000000
 = 15 :@0.844088:0.248964:0.888067:0.248964:0.888067:0.231326:0.844088:0.231326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.888074:0.248967:0.912050:0.248967:0.912050:0.231314:0.888074:0.231314:0.000000:0.000000
ap :@0.727422:0.268436:0.749364:0.268436:0.749364:0.252254:0.727422:0.252254:0.000000:0.000000:0.000000
= 6,9 :@0.749364:0.268436:0.789589:0.268436:0.789589:0.252267:0.749364:0.252267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.789587:0.268741:0.813563:0.268741:0.813563:0.251088:0.789587:0.251088:0.000000:0.000000
2 :@0.361800:0.714135:0.373962:0.714135:0.373962:0.698944:0.361800:0.698944:0.000000:0.000000
R:@0.373962:0.714135:0.382735:0.714135:0.382735:0.698932:0.373962:0.698932:0.000000
R:@0.518491:0.705516:0.527264:0.705516:0.527264:0.690312:0.518491:0.690312:0.000000
R:@0.445371:0.794185:0.454144:0.794185:0.454144:0.778981:0.445371:0.778981:0.000000
 = 30 :@0.454144:0.794185:0.492021:0.794185:0.492021:0.778994:0.454144:0.778994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.492021:0.794185:0.512671:0.794185:0.512671:0.778981:0.492021:0.778981:0.000000:0.000000
 :@0.512671:0.794185:0.516227:0.794185:0.516227:0.778994:0.512671:0.778994:0.000000
Solución:@0.605543:0.687728:0.671676:0.687728:0.671676:0.671058:0.605543:0.671058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debemos restar el volumen de la esfera :@0.605543:0.711512:0.889846:0.711512:0.889846:0.695078:0.605543:0.695078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del volumen del cilindro.:@0.605543:0.728153:0.784645:0.728153:0.784645:0.711720:0.605543:0.711720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinaria :@0.078581:0.142274:0.201990:0.142274:0.201990:0.126868:0.078581:0.126868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.078581:0.157403:0.164074:0.157403:0.164074:0.142463:0.078581:0.142463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y geometría:@0.078581:0.172532:0.158194:0.172532:0.158194:0.157592:0.078581:0.157592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los silos son grandes :@0.080953:0.203052:0.221097:0.203052:0.221097:0.188112:0.080953:0.188112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tanques que sirven para :@0.080953:0.218181:0.241129:0.218181:0.241129:0.203241:0.080953:0.203241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
almacenar granos  :@0.080953:0.233310:0.204248:0.233310:0.204248:0.218370:0.080953:0.218370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y semillas.:@0.080953:0.248439:0.145529:0.248439:0.145529:0.233499:0.080953:0.233499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La forma cónica inferior :@0.080953:0.270716:0.237245:0.270716:0.237245:0.255776:0.080953:0.255776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resulta apropiada para :@0.080953:0.285845:0.229631:0.285845:0.229631:0.270905:0.080953:0.270905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
descargar lo almacenado :@0.080953:0.300974:0.248258:0.300974:0.248258:0.286034:0.080953:0.286034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del tanque.:@0.080953:0.316103:0.154264:0.316103:0.154264:0.301163:0.080953:0.301163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por su forma geométrica, :@0.080953:0.338380:0.247721:0.338380:0.247721:0.323440:0.080953:0.323440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es muy útil al momento de :@0.080953:0.353509:0.260070:0.353509:0.260070:0.338569:0.080953:0.338569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
saber acerca del volumen :@0.080953:0.368638:0.251220:0.368638:0.251220:0.353698:0.080953:0.353698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de semillas o granos :@0.080953:0.383767:0.216663:0.383767:0.216663:0.368827:0.080953:0.368827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
almacenados.:@0.080953:0.398896:0.170680:0.398896:0.170680:0.383956:0.080953:0.383956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.485302:0.187141:0.485302:0.187141:0.468355:0.078581:0.468355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.501944:0.176057:0.501944:0.176057:0.484997:0.078581:0.484997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entre el volumen del :@0.082576:0.521542:0.219581:0.521542:0.219581:0.506603:0.082576:0.506603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cono, la esfera y el cilindro :@0.082576:0.536671:0.253879:0.536671:0.253879:0.521732:0.082576:0.521732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se pueden establecer :@0.082576:0.551800:0.224446:0.551800:0.224446:0.536861:0.082576:0.536861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relaciones siempre que :@0.082576:0.566929:0.235579:0.566929:0.235579:0.551989:0.082576:0.551989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sus medidas sean las :@0.082576:0.582058:0.219827:0.582058:0.219827:0.567118:0.082576:0.567118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
indicadas en el gráfico. :@0.082576:0.597187:0.232014:0.597187:0.232014:0.582247:0.082576:0.582247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2r:@0.108912:0.674462:0.116574:0.674462:0.116574:0.666201:0.108912:0.666201:0.000000:0.000000
2r:@0.207675:0.673436:0.215337:0.673436:0.215337:0.665175:0.207675:0.665175:0.000000:0.000000
2r:@0.158189:0.649757:0.165852:0.649757:0.165852:0.641497:0.158189:0.641497:0.000000:0.000000
2r:@0.241043:0.633099:0.248705:0.633099:0.248705:0.624838:0.241043:0.624838:0.000000:0.000000
2r:@0.097393:0.633099:0.105055:0.633099:0.105055:0.624838:0.097393:0.624838:0.000000:0.000000
Volumen cono =:@0.093817:0.695287:0.156721:0.696538:0.156721:0.688278:0.093817:0.687027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Volumen:@0.159120:0.686972:0.193336:0.686972:0.193336:0.678711:0.159120:0.678711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esfera:@0.164912:0.692696:0.187543:0.692696:0.187543:0.684436:0.164912:0.684436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.195963:0.696318:0.201399:0.696318:0.201399:0.688058:0.195963:0.688058:0.000000
2:@0.173882:0.699834:0.178562:0.699834:0.178562:0.691574:0.173882:0.691574:0.000000
Volumen:@0.203382:0.686976:0.237598:0.686976:0.237598:0.678715:0.203382:0.678715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cilindro:@0.206183:0.692701:0.234798:0.692701:0.234798:0.684440:0.206183:0.684440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.218149:0.699834:0.222828:0.699834:0.222828:0.691574:0.218149:0.691574:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000