{"id":8268,"date":"2020-08-28T16:53:18","date_gmt":"2020-08-28T19:53:18","guid":{"rendered":"http:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/?p=8268"},"modified":"2020-08-28T16:53:18","modified_gmt":"2020-08-28T19:53:18","slug":"capitulo-5-tema-4-4","status":"publish","type":"post","link":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/?p=8268","title":{"rendered":"CAP\u00cdTULO 5 \/ TEMA 4"},"content":{"rendered":"<h1>Cuerpos geom\u00e9tricos<\/h1>\n<p style=\"text-align: justify;\"><span style=\"color: #808080;\"><em><strong>Uno de los objetos de estudio de la geometr\u00eda son los cuerpos geom\u00e9tricos. Una pelota de f\u00fatbol, un cono de helado o un dado son algunos objetos cotidianos que podemos asociar con estos cuerpos, los cuales se caracterizan por ocupar volumen en el espacio y estar formados con figuras geom\u00e9tricas.<\/strong><\/em><\/span><\/p>\n<h2 style=\"text-align: justify;\">Principales cuerpos geom\u00e9tricos<\/h2>\n<p>Los <strong>cuerpos geom\u00e9tricos<\/strong> son infinitos y cada uno posee caracter\u00edsticas propias. Los m\u00e1s comunes son el <strong>cubo<\/strong>, el<strong> prisma<\/strong>, la <strong>pir\u00e1mide<\/strong>, el <strong>cilindro<\/strong>, el<strong> cono<\/strong> y la <strong>esfera<\/strong>. Ellos se clasifican en <strong>poliedros<\/strong>\u00a0y\u00a0<strong>cuerpos redondos<\/strong>.<\/p>\n<ul>\n<li>Los <strong>poliedros<\/strong> son cuerpos geom\u00e9tricos. Todas sus caras son planas. Estos, a su vez, pueden ser <strong>regulares<\/strong> si sus caras son todas iguales o <strong>irregulares<\/strong> cuando son diferentes. Un ejemplo de poliedro es el cubo.<\/li>\n<li>Los <strong>cuerpos redondos<\/strong> son cuerpos geom\u00e9tricos con al menos una cara curva, como sucede con el cilindro.<\/li>\n<\/ul>\n<p><a href=\"https:\/\/elbibliote.com:8443\/bibliote-com-web\/others\/infographics.jsp?resourceUrl=prismas_rgb_baja.jpg\">VER INFOGRAF\u00cdA<\/a><\/p>\n<div class=\"su-box su-box-style-default sabiasque\" id=\"\" style=\"border-color:#0085be;border-radius:0px;\"><div class=\"su-box-title\" style=\"background-color:#00b8f1;color:#FFFFFF;border-top-left-radius:0px;border-top-right-radius:0px\">\u00bfSab\u00edas qu\u00e9?<\/div><div class=\"su-box-content su-u-clearfix su-u-trim\" style=\"border-bottom-left-radius:0px;border-bottom-right-radius:0px\">Al cubo tambi\u00e9n se lo denomina hexaedro regular.<\/div><\/div>\n<h2>Elementos de los cuerpos geom\u00e9tricos<\/h2>\n<p>En la mayor\u00eda de los cuerpos geom\u00e9tricos se pueden identificar los siguientes elementos.<\/p>\n<ul>\n<li style=\"text-align: justify;\"><strong>Cara:<\/strong> corresponde a cada una de las superficies planas que delimitan al cuerpo geom\u00e9trico. Pueden ser<strong> caras basales,<\/strong> las que sirven de apoyo (base) al cuerpo en el plano, o <strong>caras laterales,<\/strong> que corresponden a las de los costados.<\/li>\n<li style=\"text-align: justify;\"><strong>V\u00e9rtice:<\/strong> es el punto en el que se juntan tres o m\u00e1s caras.<\/li>\n<li style=\"text-align: justify;\"><strong>Arista:<\/strong> es el segmento de l\u00ednea que se forma cuando dos caras se juntan.<\/li>\n<\/ul>\n<div class=\"su-note destacado\"  style=\"border-color:#009ed7;\"><div class=\"su-note-inner su-u-clearfix su-u-trim\" style=\"background-color:#00b8f1;border-color:#ccffff;color:#ffffff;\"><strong>La esfera y sus curiosidades <\/strong><\/p>\n<p style=\"text-align: justify;\">La esfera es un cuerpo geom\u00e9trico que no posee ni caras, ni aristas ni v\u00e9rtice. Y se caracteriza porque todos los puntos de su superficie est\u00e1n a la misma distancia del centro. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8273 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-497015991.jpg\" alt=\"\" width=\"1080\" height=\"720\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-497015991.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-497015991-300x200.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-497015991-768x512.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-497015991-1024x683.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/div><\/div>\n<h2>Volumen de cuerpos geom\u00e9tricos<\/h2>\n<p>De acuerdo a su tipo, cada cuerpo geom\u00e9trico tiene caracter\u00edsticas propias que permiten calcular su volumen a trav\u00e9s de f\u00f3rmulas.<\/p>\n<table style=\"width: 669.5px;\">\n<tbody>\n<tr style=\"height: 22px;\">\n<td style=\"background-color: #97dbde; text-align: center; height: 22px; width: 52px;\"><strong>Nombre<\/strong><\/td>\n<td style=\"background-color: #97dbde; text-align: center; height: 22px; width: 206px;\"><strong>Figura<\/strong><\/td>\n<td style=\"background-color: #97dbde; text-align: center; height: 22px; width: 384.5px;\"><strong>F\u00f3rmula de volumen<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 205px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 205px;\"><strong>Cubo<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; text-align: center; height: 205px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8376 alignnone\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2-300x300.jpg\" alt=\"\" width=\"191\" height=\"191\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2-300x300.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2-150x150.jpg 150w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2-768x768.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2-1024x1024.jpg 1024w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-2.jpg 1080w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 205px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V=l^{3}}\" alt=\"\\boldsymbol{V=l^{3}}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em> <\/strong>= volumen<\/p>\n<p><strong><em>l<\/em><\/strong> = lado<\/td>\n<\/tr>\n<tr style=\"height: 208px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 208px;\"><strong>Prisma<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; text-align: center; height: 208px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8379 alignnone\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-2-181x300.jpg\" alt=\"\" width=\"117\" height=\"194\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-2-181x300.jpg 181w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-2-768x1271.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-2-619x1024.jpg 619w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-2.jpg 1080w\" sizes=\"(max-width: 117px) 100vw, 117px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 208px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V&amp;space;=&amp;space;A_{b}\\times&amp;space;h}\" alt=\"\\boldsymbol{V = A_{b}\\times h}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em><\/strong> = volumen<br \/>\n<strong><em>A<sub>b<\/sub><\/em><\/strong> = \u00e1rea basal<\/p>\n<p><strong><em>h<\/em><\/strong> = altura<\/td>\n<\/tr>\n<tr style=\"height: 164px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 164px;\"><strong>Pir\u00e1mide<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; height: 164px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8378 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-2-300x291.jpg\" alt=\"\" width=\"156\" height=\"151\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-2-300x291.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-2-768x745.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-2-1024x994.jpg 1024w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-2.jpg 1080w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 164px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V&amp;space;=&amp;space;\\frac{A_{b}\\times&amp;space;h}{3}}\" alt=\"\\boldsymbol{V = \\frac{A_{b}\\times h}{3}}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em> <\/strong>= volumen<\/p>\n<p><strong><em>A<sub>b<\/sub><\/em><\/strong> = \u00e1rea basal<\/p>\n<p><strong><em>h<\/em><\/strong> = altura<\/td>\n<\/tr>\n<tr style=\"height: 224px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 224px;\"><strong>Cilindro<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; text-align: center; height: 224px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8374 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-2-124x300.jpg\" alt=\"\" width=\"87\" height=\"210\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-2-124x300.jpg 124w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-2-768x1857.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-2-423x1024.jpg 423w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-2.jpg 1080w\" sizes=\"(max-width: 87px) 100vw, 87px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 224px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V&amp;space;=\\pi&amp;space;\\times&amp;space;r^{2}\\times&amp;space;h}\" alt=\"\\boldsymbol{V =\\pi \\times r^{2}\\times h}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em><\/strong> = volumen<\/p>\n<p><strong><em>\u03c0<\/em><\/strong> = n\u00famero pi (3,14&#8230;)<\/p>\n<p><strong><em>r<\/em><\/strong> = radio<\/p>\n<p><strong><em>h<\/em><\/strong> = altura<\/td>\n<\/tr>\n<tr style=\"height: 186px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 186px;\"><strong>Cono<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; text-align: center; height: 186px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8375 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-2-293x300.jpg\" alt=\"\" width=\"144\" height=\"147\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-2-293x300.jpg 293w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-2-768x786.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-2-1000x1024.jpg 1000w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-2.jpg 1080w\" sizes=\"(max-width: 144px) 100vw, 144px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 186px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V&amp;space;=\\frac{\\pi&amp;space;\\times&amp;space;r^{2}\\times&amp;space;h}{3}}\" alt=\"\\boldsymbol{V =\\frac{\\pi \\times r^{2}\\times h}{3}}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em><\/strong> = volumen<\/p>\n<p><strong><em>\u03c0<\/em><\/strong> = n\u00famero pi (3,14&#8230;)<\/p>\n<p><strong><em>r<\/em><\/strong> = radio<\/p>\n<p><strong><em>h<\/em><\/strong> = altura<\/td>\n<\/tr>\n<tr style=\"height: 184px;\">\n<td style=\"width: 52px; vertical-align: middle; text-align: center; height: 184px;\"><strong>Esfera<\/strong><\/td>\n<td style=\"width: 206px; vertical-align: middle; text-align: center; height: 184px;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8377 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Esfera-293x300.jpg\" alt=\"\" width=\"142\" height=\"145\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Esfera-293x300.jpg 293w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Esfera-768x786.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Esfera-1000x1024.jpg 1000w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Esfera.jpg 1080w\" sizes=\"(max-width: 142px) 100vw, 142px\" \/><\/td>\n<td style=\"width: 384.5px; vertical-align: middle; height: 184px;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\boldsymbol{V&amp;space;=\\frac{4}{3}\\times&amp;space;\\pi&amp;space;\\times&amp;space;r^{3}}\" alt=\"\\boldsymbol{V =\\frac{4}{3}\\times \\pi \\times r^{3}}\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Donde:<\/p>\n<p><strong><em>V<\/em><\/strong> = volumen<\/p>\n<p><strong><em>\u03c0<\/em><\/strong> = n\u00famero pi (3,14&#8230;)<\/p>\n<p><strong><em>r<\/em><\/strong> = radio<\/p>\n<p><strong><em>h<\/em><\/strong> = altura<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/elbibliote.com:8443\/bibliote-com-web\/others\/infographics.jsp?resourceUrl=area_y_volumen_rgb_baja.jpg\">VER INFOGRAF\u00cdA<\/a><\/p>\n<p><strong>&#8211; Calcula el volumen de este cubo.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8354 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura-2.jpg\" alt=\"\" width=\"236\" height=\"200\" \/><\/p>\n<p style=\"text-align: justify;\">Un cubo se caracteriza porque todos sus lados miden lo mismo, de manera que al conocer solo la medida de un lado se puede aplicar la f\u00f3rmula:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V=l^{3}\" alt=\"V=l^{3}\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V=(3\\,&amp;space;cm)^{3}\" alt=\"V=(3\\, cm)^{3}\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V=\\mathbf{27\\,&amp;space;cm^{3}}\" alt=\"V=\\mathbf{27\\, cm^{3}}\" align=\"absmiddle\" \/><\/p>\n<p>&#8211; <strong>Calcula el volumen del siguiente cilindro.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8353 aligncenter\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/cilin.jpg\" alt=\"\" width=\"253\" height=\"251\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/cilin.jpg 253w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/cilin-150x150.jpg 150w\" sizes=\"(max-width: 253px) 100vw, 253px\" \/><\/p>\n<p style=\"text-align: justify;\">Seg\u00fan la f\u00f3rmula, los \u00fanicos datos que se necesitan son el radio del cilindro y su altura. De la imagen se obtienen los datos:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V&amp;space;=\\pi&amp;space;\\times&amp;space;r^{2}\\times&amp;space;h\" alt=\"V =\\pi \\times r^{2}\\times h\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V&amp;space;=\\pi&amp;space;\\times&amp;space;(2\\,&amp;space;cm)^{2}\\times&amp;space;6\\,&amp;space;cm\" alt=\"V =\\pi \\times (2\\, cm)^{2}\\times 6\\, cm\" align=\"absmiddle\" \/><\/p>\n<p>En este caso observa que el radio est\u00e1 elevado al cuadrado, por lo tanto, al resolver esa potencia las unidades tambi\u00e9n se ver\u00e1n afectadas, por lo que quedar\u00e1n cent\u00edmetros cuadrados:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V&amp;space;=\\pi&amp;space;\\times&amp;space;4\\,&amp;space;cm^{2}\\times&amp;space;6\\,&amp;space;cm\" alt=\"V =\\pi \\times 4\\, cm^{2}\\times 6\\, cm\" align=\"absmiddle\" \/><\/p>\n<p style=\"text-align: justify;\">El n\u00famero pi (\u03c0) es un n\u00famero irracional, por lo cual es infinito. Para efectos de estos c\u00e1lculos, usaremos solamente 2 de sus decimales, es decir, lo aproximamos a 3,14.<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V&amp;space;=3,14&amp;space;\\times&amp;space;4\\,&amp;space;cm^{2}\\times&amp;space;6\\,&amp;space;cm\" alt=\"V =3,14 \\times 4\\, cm^{2}\\times 6\\, cm\" align=\"absmiddle\" \/><\/p>\n<p>Al resolver este producto se obtiene el volumen del cilindro.<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/svg.latex?V&amp;space;=\\mathbf{75,36\\,&amp;space;cm^{3}}\" alt=\"V =\\mathbf{75,36\\, cm^{3}}\" align=\"absmiddle\" \/><\/p>\n<div class=\"su-box su-box-style-default sabiasque\" id=\"\" style=\"border-color:#0085be;border-radius:0px;\"><div class=\"su-box-title\" style=\"background-color:#00b8f1;color:#FFFFFF;border-top-left-radius:0px;border-top-right-radius:0px\">\u00bfSab\u00edas qu\u00e9?<\/div><div class=\"su-box-content su-u-clearfix su-u-trim\" style=\"border-bottom-left-radius:0px;border-bottom-right-radius:0px\">Cuando se usan m\u00faltiplos o subm\u00faltiplos del metro, el volumen siempre se expresa en unidades c\u00fabicas: m<sup>3<\/sup>, cm<sup>3<\/sup>, mm<sup>3<\/sup>, km<sup>3<\/sup>, etc.<\/div><\/div>\n<figure id=\"attachment_8518\" aria-describedby=\"caption-attachment-8518\" style=\"width: 1080px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8518 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1.jpg\" alt=\"\" width=\"1080\" height=\"1080\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1-150x150.jpg 150w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1-300x300.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1-768x768.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock-936297088-1-1024x1024.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><figcaption id=\"caption-attachment-8518\" class=\"wp-caption-text\">Los prismas son poliedros cuyos lados laterales son paralelogramos y con dos caras paralelas e iguales denominadas bases. Reciben su nombre de acuerdo a la forma de su base, por ejemplo, si su base es un tri\u00e1ngulo, se denomina prisma triangular, si es un pent\u00e1gono se denomina prisma pentagonal y as\u00ed sucesivamente. Un paralelep\u00edpedo es un prisma cuya base es un paralelogramo.<\/figcaption><\/figure>\n<h2>Construcci\u00f3n de cuerpos geom\u00e9tricos<\/h2>\n<p style=\"text-align: justify;\">Los cuerpos geom\u00e9tricos tienen volumen y, por lo tanto, se pueden representar en tres dimensiones: largo, alto y ancho. Las im\u00e1genes a continuaci\u00f3n son patrones que puedes usar para construir los cuerpos geom\u00e9tricos m\u00e1s comunes:<\/p>\n<h3>Cubo<strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8396 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-1.jpg\" alt=\"\" width=\"1080\" height=\"850\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-1-300x236.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-1-768x604.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cubo-1-1024x806.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/strong><br \/>\n<strong>Prisma rectangular<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8398 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-1.jpg\" alt=\"\" width=\"1080\" height=\"1156\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-1-280x300.jpg 280w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-1-768x822.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Prisma-rectangular-1-957x1024.jpg 957w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><br \/>\n<\/strong><strong>Pir\u00e1mide<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8397 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-1.jpg\" alt=\"\" width=\"1080\" height=\"1052\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-1-300x292.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-1-768x748.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Piramide-1-1024x997.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/strong><br \/>\n<strong>Cilindro<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8394 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-1.jpg\" alt=\"\" width=\"1080\" height=\"1404\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-1-231x300.jpg 231w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-1-768x998.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cilindro-1-788x1024.jpg 788w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/strong><br \/>\n<strong>Cono<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8395 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-1.jpg\" alt=\"\" width=\"1080\" height=\"892\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-1.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-1-300x248.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-1-768x634.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Cono-1-1024x846.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/strong><\/h3>\n<figure id=\"attachment_8519\" aria-describedby=\"caption-attachment-8519\" style=\"width: 1080px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8519 size-full\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock_33757074_XXXLARGE-Profesor-y-estudiante-en-la-leccion.jpg\" alt=\"\" width=\"1080\" height=\"720\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock_33757074_XXXLARGE-Profesor-y-estudiante-en-la-leccion.jpg 1080w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock_33757074_XXXLARGE-Profesor-y-estudiante-en-la-leccion-300x200.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock_33757074_XXXLARGE-Profesor-y-estudiante-en-la-leccion-768x512.jpg 768w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/iStock_33757074_XXXLARGE-Profesor-y-estudiante-en-la-leccion-1024x683.jpg 1024w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><figcaption id=\"caption-attachment-8519\" class=\"wp-caption-text\">La construcci\u00f3n de cuerpos geom\u00e9tricos, adem\u00e1s de su gran utilidad al momento de representar a estas figuras, permite trasladar estos conocimientos a otras \u00e1reas como la arquitectura y la ingenier\u00eda, en las cuales se realizan dise\u00f1os a escalas. Conocer las diferentes f\u00f3rmulas de c\u00e1lculo y volumen de las figuras es fundamental para realizar operaciones m\u00e1s avanzadas.<\/figcaption><\/figure>\n<p style=\"text-align: justify;\"><div class=\"su-note destacado\"  style=\"border-color:#009ed7;\"><div class=\"su-note-inner su-u-clearfix su-u-trim\" style=\"background-color:#00b8f1;border-color:#ccffff;color:#ffffff;\">\n<h3 style=\"text-align: justify;\"><strong>\u00a1A practicar!<\/strong><\/h3>\n<p style=\"text-align: justify;\"><strong>1. Calcula el volumen de los siguientes cuerpos geom\u00e9tricos.<\/strong><\/p>\n<p style=\"text-align: justify;\">a) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-8731\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura5-1-300x278.jpg\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura5-1-300x278.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura5-1.jpg 497w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0 *La base es un rect\u00e1ngulo.<br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 133,33 cm<sup>3<\/sup><\/div><\/div>\n<p style=\"text-align: justify;\">b) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-8732\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura6-1-300x276.jpg\" alt=\"\" width=\"300\" height=\"276\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura6-1-300x276.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura6-1.jpg 311w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 64 cm<sup>3<\/sup><\/div><\/div>\n<p style=\"text-align: justify;\">c) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8729\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura3-1.jpg\" alt=\"\" width=\"244\" height=\"247\" \/><br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 904,32 cm<sup>3<\/sup><\/div><\/div>\n<p style=\"text-align: justify;\">d)\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8730\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura4.jpg\" alt=\"\" width=\"287\" height=\"285\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura4.jpg 287w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura4-150x150.jpg 150w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 33,49 cm<sup>3<\/sup><\/div><\/div>\n<p>e) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-8727\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura-3-300x164.jpg\" alt=\"\" width=\"300\" height=\"164\" srcset=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura-3-300x164.jpg 300w, https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura-3.jpg 363w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 96 cm<sup>3<\/sup><\/div><\/div>\n<p>f) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8728\" src=\"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/wp-content\/uploads\/2020\/08\/Captura2-1.jpg\" alt=\"\" width=\"209\" height=\"238\" \/><br \/>\n<div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus respuestas su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Soluci\u00f3n<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">V = 62,8 cm<sup>3<\/sup><\/div><\/div>\n<p style=\"text-align: justify;\"><\/div><\/div>\n<p style=\"text-align: justify;\"><div class=\"su-spoiler su-spoiler-style-simple su-spoiler-icon-plus material_docente su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>RECURSOS PARA DOCENTES<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<h3 style=\"text-align: justify;\">Art\u00edculo &#8220;Poliedros irregulares&#8221;<\/h3>\n<p style=\"text-align: justify;\">El art\u00edculo explica qu\u00e9 es un poliedro y qu\u00e9 caracteriza a los irregulares. Tambi\u00e9n hace una breve explicaci\u00f3n de los s\u00f3lidos plat\u00f3nicos y muestra algunos ejemplos.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/elbibliote.com\/resources\/Temas\/html\/1116.php\">VER<\/a><\/p>\n<h3 style=\"text-align: justify;\">Infograf\u00eda &#8220;Cuerpos redondos&#8221;<\/h3>\n<p style=\"text-align: justify;\">La infograf\u00eda explica de manera sencilla qu\u00e9 es un cuerpo redondo, sus caracter\u00edsticas y su presencia en la vida cotidiana.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/elbibliote.com:8443\/bibliote-com-web\/others\/infographics.jsp?resourceUrl=cuerpos_redondos_rgb_baja.jpg\">VER<\/a><\/p>\n<h3 style=\"text-align: justify;\">Art\u00edculo &#8220;Volumen de figuras geom\u00e9tricas&#8221;<\/h3>\n<p style=\"text-align: justify;\">En este art\u00edculo destacado se explica qu\u00e9 es el volumen y c\u00f3mo calcularlo en los diferentes cuerpos geom\u00e9tricos. Tambi\u00e9n se plantean una serie de problemas resueltos y de ejercicios planteados.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/elbibliote.com\/resources\/Temas\/html\/1920.php\">VER<\/a><\/p>\n<p style=\"text-align: justify;\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Uno de los objetos de estudio de la geometr\u00eda son los cuerpos geom\u00e9tricos. Una pelota de f\u00fatbol, un cono de helado o un dado son algunos objetos cotidianos que podemos asociar con estos cuerpos, los cuales se caracterizan por ocupar volumen en el espacio y estar formados con figuras geom\u00e9tricas.<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[475,1204,470,320,538,1609,583,783,457,82,42,321,177,315,569,551,811,275,11,1298,468,1309,43,1455,1610,472,782],"class_list":["post-8268","post","type-post","status-publish","format-standard","hentry","category-7mo-grado","tag-aristas","tag-calculo","tag-caras","tag-cilindros","tag-clasificacion","tag-conos","tag-construcciones","tag-cubos","tag-cuerpos","tag-ejemplos","tag-ejercicios","tag-esferas","tag-figuras","tag-formas","tag-formulas","tag-geometrias","tag-geometricas","tag-geometricos","tag-matematicas","tag-piramides","tag-poliedros","tag-prismas","tag-problemas","tag-redondos","tag-tipo","tag-vertices","tag-volumenes"],"_links":{"self":[{"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/posts\/8268"}],"collection":[{"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8268"}],"version-history":[{"count":18,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/posts\/8268\/revisions"}],"predecessor-version":[{"id":9905,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=\/wp\/v2\/posts\/8268\/revisions\/9905"}],"wp:attachment":[{"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/elbibliote.com\/libro-pedia\/manual_matematica\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}