{"id":4745,"date":"2022-09-01T14:57:39","date_gmt":"2022-09-01T12:57:39","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/objem-kruhu-priklad-1\/"},"modified":"2022-09-01T14:57:39","modified_gmt":"2022-09-01T12:57:39","slug":"objem-kruhu-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/objem-kruhu-priklad-1\/","title":{"rendered":"Objem kruhu &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Obd\u00e9ln\u00edk ABCD m\u00e1 n\u00e1sleduj\u00edc\u00ed vrcholy: <em><strong>A [-3; -1]<\/strong><\/em>, <em><strong>B [-2; -1]<\/strong><\/em>, <strong><em>C [2; 1]<\/em><\/strong>, <em><strong>D [1; 3]<\/strong><\/em>. K obd\u00e9ln\u00edku je opsan\u00e1 kru\u017enice <strong><em>k<\/em><\/strong>.<\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone  wp-image-4744\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/kruh-300x278.png\" alt=\"\" width=\"387\" height=\"359\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/kruh-300x278.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/kruh-300x278.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/kruh.png 388w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p><strong>Jak\u00fd je obsah kruhu ohrani\u010den\u00e9ho kru\u017enic\u00ed k?<\/strong><br \/>$$a) 25 \u03c0$$<br \/>$$b) \\frac{94}{5}\u03c0$$<br \/>$$c) \\frac{25}{2}\u03c0$$<br \/>$$d) 5 \u03c0$$<br \/>$$e) \\frac{25}{4}\u03c0$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>St\u0159ed opsan\u00e9 kru\u017enice je v pr\u016fse\u010d\u00edku \u00fahlop\u0159\u00ed\u010dek obd\u00e9ln\u00edku ABCD. Pr\u016fse\u010d\u00edk je v polovin\u011b \u00fahlop\u0159\u00ed\u010dek AC i BD.<\/p>\n<p>1) Jsme schopni z obr\u00e1zku poznat d\u00e9lku \u00fase\u010dky AC, kter\u00e1 jest 5 cm. Polom\u011br na\u0161\u00ed opsan\u00e9 kru\u017enice bude tedy polovina, tj. 2,5 cm. Nyn\u00ed m\u016f\u017eeme po\u010d\u00edtat obsah kruhu:<br \/>$$S=\u03c0\\cdot r^{2}$$<br \/>2) Dosad\u00edme<br \/>$$S=\u03c0\\cdot 2,5^{2}$$<br \/>3) Umocn\u00edme \u010d\u00edslo<br \/>$$S=\\frac{25}{4}\u03c0$$<br \/><strong>Spr\u00e1vn\u011b je tedy odpov\u011b\u010f E.<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 3-5 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-4745","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Objem kruhu - 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-kruhu-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Objem kruhu - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Obd\u00e9ln\u00edk ABCD m\u00e1 n\u00e1sleduj\u00edc\u00ed vrcholy: A [-3; -1], B [-2; -1], C [2; 1], D [1; 3]. K obd\u00e9ln\u00edku je opsan\u00e1 kru\u017enice k. Jak\u00fd je obsah kruhu ohrani\u010den\u00e9ho kru\u017enic\u00ed k?$$a) 25 \u03c0$$$$b) frac{94}{5}\u03c0$$$$c) frac{25}{2}\u03c0$$$$d) 5 \u03c0$$$$e) frac{25}{4}\u03c0$$ \u0158e\u0161en\u00ed: St\u0159ed opsan\u00e9 kru\u017enice je v pr\u016fse\u010d\u00edku \u00fahlop\u0159\u00ed\u010dek obd\u00e9ln\u00edku ABCD. Pr\u016fse\u010d\u00edk je v polovin\u011b \u00fahlop\u0159\u00ed\u010dek AC i ... 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K obd\u00e9ln\u00edku je opsan\u00e1 kru\u017enice k. Jak\u00fd je obsah kruhu ohrani\u010den\u00e9ho kru\u017enic\u00ed k?$$a) 25 \u03c0$$$$b) frac{94}{5}\u03c0$$$$c) frac{25}{2}\u03c0$$$$d) 5 \u03c0$$$$e) frac{25}{4}\u03c0$$ \u0158e\u0161en\u00ed: St\u0159ed opsan\u00e9 kru\u017enice je v pr\u016fse\u010d\u00edku \u00fahlop\u0159\u00ed\u010dek obd\u00e9ln\u00edku ABCD. Pr\u016fse\u010d\u00edk je v polovin\u011b \u00fahlop\u0159\u00ed\u010dek AC i ... 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