{"id":4729,"date":"2022-09-01T14:13:36","date_gmt":"2022-09-01T12:13:36","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/objem-a-povrch-kuzele-priklad-1\/"},"modified":"2022-09-01T14:19:13","modified_gmt":"2022-09-01T12:19:13","slug":"objem-a-povrch-kuzele-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/objem-a-povrch-kuzele-priklad-1\/","title":{"rendered":"Objem a povrch ku\u017eele &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:&nbsp;<\/strong>M\u00e1me sklenici ve tvaru rota\u010dn\u00edho ku\u017eele. Voda, kter\u00e1 je v n\u00ed m\u00e1 objem 40,5\u03c0 cm\u00b3 a nesah\u00e1 a\u017e po okraj sklenice, ale jen 6 cm od vrcholu sklenice (spodek sklenice).<\/p>\n<p>Jak\u00fd je obsah plochy sklenice sm\u00e1\u010den\u00e9 vodou?<br \/>(Zaokrouhlete na desetiny cm \u010dtvere\u010dn\u00edch)<br \/>a) 51,9 cm\u00b2<br \/>b) 54,3 cm\u00b2<br \/>c) 106,0 cm\u00b2<br \/>d) 169,5 cm\u00b2<br \/>e) 211,9 cm\u00b2<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Nejd\u0159\u00edve po\u010d\u00edt\u00e1me podle vzorce na objem ku\u017eele, abychom zjistili polom\u011br, kter\u00fd budete pot\u0159ebovat pro v\u00fdpo\u010det povrchu:<br \/>$$V=\\frac{1}{3}\u03c0\\cdot r^{2}\\cdot v$$<br \/>2) Dosad\u00edme:<br \/>$$40,5\u03c0 =\\frac{1}{3}\u03c0\\cdot r^{2}\\cdot 6$$<br \/>3) Ludolfovo \u010d\u00edslo se n\u00e1m na obou stran\u00e1ch anuluje; d\u00e1le mus\u00edme d\u00e1t pravou stranu na stejn\u00e9ho jmenovatele, tedy mus\u00edme \u010d\u00edslo vyn\u00e1sobit 3; v\u00fdsledek pak mus\u00edme vyd\u011blit 6, proto\u017ee ji p\u0159ev\u00e1d\u00edme na druhou stranu m\u00e1 opa\u010dn\u00fd efekt<br \/>$$r^{2} = 20,25$$<br \/>4) Odmocn\u00edme:<br \/>$$r=4,5cm$$<br \/>5) Nyn\u00ed m\u016f\u017eeme vypo\u010d\u00edtat pr\u016fm\u011br dle vzorce:<br \/>$$d^{2} = r^{2} + v^{2}$$<br \/>6) Dosad\u00edme:<br \/>$$d^{2} = 4,5^{2} + 6^{2}$$<br \/>7) Na prav\u00e9 stran\u011b se zbav\u00edme mocnin a umocn\u00edme \u010d\u00edsla<br \/>$$d^{2} = 56,25$$<br \/>8) V\u00fdslek odmocn\u00edme, aby n\u00e1m vych\u00e1zel pro 1d<br \/>$$d = 7,5 cm$$<br \/>9) Kone\u010dn\u011b se dost\u00e1v\u00e1me k v\u00fdpo\u010dtu plochy sklenice, pou\u017eijeme vzore\u010dek:<br \/>$$S=\u03c0\\cdot r\\cdot d$$<br \/>10) Dosad\u00edme:<br \/>$$S=\u03c0\\cdot 4,5\\cdot 7,5$$<br \/>11) Zb\u00fdv\u00e1 u\u017e jen vyn\u00e1sobit v\u00fdsledek:<br \/>$$S=106cm^{2}$$<br \/><strong>Spr\u00e1vn\u011b je odpov\u011b\u010f (c)<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost:&nbsp;5-7 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4729","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Objem a povrch ku\u017eele - p\u0159\u00edklad 1 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/objem-a-povrch-kuzele-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Objem a povrch ku\u017eele - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed:&nbsp;M\u00e1me sklenici ve tvaru rota\u010dn\u00edho ku\u017eele. Voda, kter\u00e1 je v n\u00ed m\u00e1 objem 40,5\u03c0 cm\u00b3 a nesah\u00e1 a\u017e po okraj sklenice, ale jen 6 cm od vrcholu sklenice (spodek sklenice). Jak\u00fd je obsah plochy sklenice sm\u00e1\u010den\u00e9 vodou?(Zaokrouhlete na desetiny cm \u010dtvere\u010dn\u00edch)a) 51,9 cm\u00b2b) 54,3 cm\u00b2c) 106,0 cm\u00b2d) 169,5 cm\u00b2e) 211,9 cm\u00b2 \u0158e\u0161en\u00ed: Nejd\u0159\u00edve po\u010d\u00edt\u00e1me podle ... 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Voda, kter\u00e1 je v n\u00ed m\u00e1 objem 40,5\u03c0 cm\u00b3 a nesah\u00e1 a\u017e po okraj sklenice, ale jen 6 cm od vrcholu sklenice (spodek sklenice). Jak\u00fd je obsah plochy sklenice sm\u00e1\u010den\u00e9 vodou?(Zaokrouhlete na desetiny cm \u010dtvere\u010dn\u00edch)a) 51,9 cm\u00b2b) 54,3 cm\u00b2c) 106,0 cm\u00b2d) 169,5 cm\u00b2e) 211,9 cm\u00b2 \u0158e\u0161en\u00ed: Nejd\u0159\u00edve po\u010d\u00edt\u00e1me podle ... 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