{"id":1468,"date":"2020-08-25T17:12:01","date_gmt":"2020-08-25T15:12:01","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1468"},"modified":"2020-08-27T12:59:31","modified_gmt":"2020-08-27T10:59:31","slug":"przekroje-graniastoslupow","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1468","title":{"rendered":"Pole powierzchni ca\u0142kowitej i obj\u0119to\u015b\u0107 graniastos\u0142up\u00f3w"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby obliczy\u0107<span style=\"color: #4472c4;\">\u00a0<strong>pole powierzchni ca\u0142kowitej graniastos\u0142upa<\/strong><\/span>\u00a0musimy doda\u0107 do siebie pola wszystkich \u015bcian graniastos\u0142upa. Czyli jest to suma p\u00f3l dw\u00f3ch podstaw oraz wszystkich \u015bcian bocznych.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"alignnone wp-image-1286 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/siatka1-228x300.png\" alt=\"\" width=\"176\" height=\"232\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/siatka1-228x300.png 228w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/siatka1.png 279w\" sizes=\"(max-width: 176px) 100vw, 176px\" \/><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{C}=2\\cdot&amp;space;P_{P}+P_{B}\" alt=\"P_{C}=2\\cdot P_{P}+P_{B}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{P}\" alt=\"P_{P}\" align=\"absmiddle\" \/> to pole powierzchni podstawy.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{B}\" alt=\"P_{B}\" align=\"absmiddle\" \/> to pole powierzchni bocznej czyli suma p\u00f3l wszystkich \u015bcian bocznych.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole powierzchni ca\u0142kowitej sze\u015bcianu<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"alignnone wp-image-1290 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/sze\u015bcianek-300x282.png\" alt=\"\" width=\"203\" height=\"190\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/sze\u015bcianek-300x282.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/sze\u015bcianek.png 318w\" sizes=\"(max-width: 203px) 100vw, 203px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{C}=6\\cdot&amp;space;P_{S}\" alt=\"P_{C}=6\\cdot P_{S}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{S}\" alt=\"P_{S}\" align=\"absmiddle\" \/> to pole powierzchni dowolnej \u015bciany sze\u015bcianu.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #4472c4;\">Obj\u0119to\u015b\u0107 graniastos\u0142upa,<\/span>\u00a0<\/strong>to iloczyn jego pola podstawy i d\u0142ugo\u015bci wysoko\u015bci graniastos\u0142upa<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?V=P_{P}\\cdot&amp;space;H\" alt=\"V=P_{P}\\cdot H\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{P}\" alt=\"P_{P}\" align=\"absmiddle\" \/> to pole powierzchni podstawy.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?H\" alt=\"H\" align=\"absmiddle\" \/> to wysoko\u015b\u0107 graniastos\u0142upa.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Obj\u0119to\u015b\u0107 sze\u015bcianu<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?V=a^{3}\" alt=\"V=a^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/>\u00a0\u2013 d\u0142ugo\u015b\u0107 kraw\u0119dzi sze\u015bcianu<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"text-decoration: underline;\">Aby obliczy\u0107 obj\u0119to\u015b\u0107 pos\u0142ugujemy si\u0119\u00a0jednostkami obj\u0119to\u015bci:<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;mm^{3}\" alt=\"1\\, mm^{3}\" align=\"absmiddle\" \/>\u00a0\u2013 1 milimetr sze\u015bcienny (sze\u015bcian o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;mm\" alt=\"1\\, mm\" align=\"absmiddle\" \/>)<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;cm^{3}\" alt=\"1\\, cm^{3}\" align=\"absmiddle\" \/>\u00a0\u2013 1 centymetr sze\u015bcienny (sze\u015bcian o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;cm\" alt=\"1\\, cm\" align=\"absmiddle\" \/>) jest to inaczej\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;ml\" alt=\"1\\, ml\" align=\"absmiddle\" \/>,\u00a0czyli jeden\u00a0<strong>mililitr<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;ml=1\\,&amp;space;cm^{3}\" alt=\"1\\, ml=1\\, cm^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\:&amp;space;ml&amp;space;=0,001\\:&amp;space;l\" alt=\"1\\: ml =0,001\\: l\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\:&amp;space;cm^{3}=1000\\:&amp;space;mm^{3}\" alt=\"1\\: cm^{3}=1000\\: mm^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;ml\" alt=\"1\\, ml\" align=\"absmiddle\" \/>\u00a0 wa\u017cy\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;g\" alt=\"1\\, g\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm^{3}\" alt=\"1\\, dm^{3}\" align=\"absmiddle\" \/>\u00a0\u2013 1 decymetr sze\u015bcienny (sze\u015bcian o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm\" alt=\"1\\, dm\" align=\"absmiddle\" \/>) jest to inaczej\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;l\" alt=\"1\\, l\" align=\"absmiddle\" \/>,\u00a0czyli jeden<strong>\u00a0litr<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;l=1\\,&amp;space;dm^{3}\" alt=\"1\\, l=1\\, dm^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\:&amp;space;dm^{3}=1000\\:&amp;space;cm^{3}\" alt=\"1\\: dm^{3}=1000\\: cm^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;l\" alt=\"1\\, l\" align=\"absmiddle\" \/>\u00a0 wa\u017cy\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;kg\" alt=\"1\\, kg\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Jeden\u00a0<strong>hektolitr<\/strong> to jednostka sto razy wi\u0119ksza od litra, zapisujemy\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;hl\" alt=\"1\\, hl\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;hl=100\\,&amp;space;l\" alt=\"1\\, hl=100\\, l\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m^{3}\" alt=\"1\\, m^{3}\" align=\"absmiddle\" \/>\u00a0\u2013 1 metr sze\u015bcienny (sze\u015bcian o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m\" alt=\"1\\, m\" align=\"absmiddle\" \/>)<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\:&amp;space;m^{3}=1000\\:&amp;space;dm^{3}=1000\\:&amp;space;l\" alt=\"1\\: m^{3}=1000\\: dm^{3}=1000\\: l\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km^{3}\" alt=\"1\\, km^{3}\" align=\"absmiddle\" \/>\u00a0\u2013 1 kilometr sze\u015bcienny (sze\u015bcian o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km\" alt=\"1\\, km\" align=\"absmiddle\" \/>)<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aby obliczy\u0107\u00a0pole powierzchni ca\u0142kowitej graniastos\u0142upa\u00a0musimy doda\u0107 do siebie pola wszystkich \u015bcian graniastos\u0142upa. Czyli jest to suma p\u00f3l dw\u00f3ch podstaw oraz wszystkich \u015bcian bocznych. to pole powierzchni podstawy. to pole powierzchni bocznej czyli suma p\u00f3l wszystkich \u015bcian bocznych. &nbsp; Pole powierzchni ca\u0142kowitej sze\u015bcianu to pole powierzchni dowolnej \u015bciany sze\u015bcianu. &nbsp; Obj\u0119to\u015b\u0107 graniastos\u0142upa,\u00a0to iloczyn jego pola podstawy [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,14],"tags":[],"class_list":["post-1468","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-vii"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pole powierzchni ca\u0142kowitej i obj\u0119to\u015b\u0107 graniastos\u0142up\u00f3w - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=1468\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pole powierzchni ca\u0142kowitej i obj\u0119to\u015b\u0107 graniastos\u0142up\u00f3w - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Aby obliczy\u0107\u00a0pole powierzchni ca\u0142kowitej graniastos\u0142upa\u00a0musimy doda\u0107 do siebie pola wszystkich \u015bcian graniastos\u0142upa. Czyli jest to suma p\u00f3l dw\u00f3ch podstaw oraz wszystkich \u015bcian bocznych. to pole powierzchni podstawy. to pole powierzchni bocznej czyli suma p\u00f3l wszystkich \u015bcian bocznych. &nbsp; Pole powierzchni ca\u0142kowitej sze\u015bcianu to pole powierzchni dowolnej \u015bciany sze\u015bcianu. &nbsp; Obj\u0119to\u015b\u0107 graniastos\u0142upa,\u00a0to iloczyn jego pola podstawy [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"http:\/\/matma.com.pl\/?p=1468\" \/>\n<meta property=\"og:site_name\" content=\"Matma.com.pl\" \/>\n<meta property=\"article:published_time\" content=\"2020-08-25T15:12:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-08-27T10:59:31+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/siatka1-228x300.png\" \/>\n<meta name=\"author\" content=\"lucynabartczak99\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucynabartczak99\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/matma.com.pl\/?p=1468#article\",\"isPartOf\":{\"@id\":\"http:\/\/matma.com.pl\/?p=1468\"},\"author\":{\"name\":\"lucynabartczak99\",\"@id\":\"https:\/\/matma.com.pl\/#\/schema\/person\/b54229c3e035dea49ef8c166c5c63f1e\"},\"headline\":\"Pole powierzchni ca\u0142kowitej i obj\u0119to\u015b\u0107 graniastos\u0142up\u00f3w\",\"datePublished\":\"2020-08-25T15:12:01+00:00\",\"dateModified\":\"2020-08-27T10:59:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/matma.com.pl\/?p=1468\"},\"wordCount\":180,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/matma.com.pl\/#organization\"},\"articleSection\":[\"Baza Wiedzy\",\"Klasa VII\"],\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/matma.com.pl\/?p=1468#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/matma.com.pl\/?p=1468\",\"url\":\"http:\/\/matma.com.pl\/?p=1468\",\"name\":\"Pole powierzchni ca\u0142kowitej i obj\u0119to\u015b\u0107 graniastos\u0142up\u00f3w - 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