Kutalika kwa piramidi. Kodi awapeze?

Piramidi - ndi polyhedron, m'munsi mwa zomwe ndi polygon. Pankhope zawo zonse nayenso mawonekedwe Triangles kuti tikumane vertex wina. Mapiramidi ndi triangular, quadrilateral ndi zina zotero. Pofuna kudziwa zimene piramidi kutsogolo kwa inu, ndi okwanira awerenge chiwerengero cha kumathandiza kupeza ngodya zabwino pa maziko ake. Tanthawuzo la "kutalika kwa piramidi" sizachilendo mu masamu mu zolinga za maphunziro. Nkhaniyi adzayesa kuganizira njira zosiyana waipeza.

mbali piramidi

Aliyense piramidi tichipeza zinthu zotsatirazi:

• nkhope mbali yomwe ndi atatu ngodya ndi converge pa vertex ndi;
• apothem akuimira kutalika wotsika kuchokera ake pamwamba;
• pamwamba pa piramidi - mfundo imene zikugwirizana m'mbali lateral, koma izi sanama mu ndege ya m'munsi ya;
• m'munsi - ndi polygon, amene sikuli kwa nsonga ya;
• kutalika kwa piramidi ndi gawo awakwiyitsa pamwamba pa piramidi ndi maziko ake ndipamene mlingo woyenerera.

Kodi kupeza kutalika kwa piramidi, ngati inu mukudziwa buku lake

Pambuyo chilinganizo piramidi buku V = (S * h) / 3 (mu chilinganizo V - buku, S - malo a m'munsi, H - kutalika kwa piramidi), ife tikupeza kuti H = (3 * V) / S. Kulimbitsa zinthu, tiyeni vutolo nthawi yomweyo. The triangular piramidi lalikulu zapansi ndi 50 cm ^2, pamene buku lake 125 masentimita ^3. kutalika Unknown wa piramidi triangular, ndi zomwe tiyenera kupeza. Ndi yosavuta: amaika deta mu dongosolo lathu. Timapeza H = (3 * 125) / 50 = 7.5 cm.

Kodi kupeza kutalika kwa piramidi, ngati ife kudziwa kutalika kwa opendekera ndi m'mbali mwake

Monga ife kumbukirani, kutalika kwa piramidi amapanga ndi m'munsi ngodya yoyenera. Izi zikutanthauza kuti msinkhu wa nthiti ndi theka diagonally pamodzi kupanga bwino-angled makona. Ambiri, ndithudi, kumbukirani Lingaliro Lovomerezeka Pythagorean. Kudziwa miyezo iwiri, phindu chachitatu chidzakhala zovuta kupeza. Kumbukirani kudziwika Lingaliro Lovomerezeka a² = b² + c², ndi m'mene - ndi hypotenuse, ndipo mu nkhani iyi m'mphepete mwa piramidi; B - mbali yoyamba kapena theka opendekera ndi - motero, mwendo wachiwiri kapena kutalika kwa piramidi. Kuyambira chilinganizo izi c² = a² - b².

Tsopano vuto: mu lamanja opendekera wa piramidi ndi 20 cm, pamene kutalika kwa m'mphepete - 30 kutalika masentimita ayenera kupezeka .. Kuthetsa: c² = 30² - 20² = 900-400 = 500. Choncho, = √ 500 = za 22,4.

Kodi kupeza kutalika kwa piramidi truncated

Ndi polygon, amene ali gawo kufanana kwa maziko ake. Kutalika kwa piramidi truncated - mbali kuti zikugwirizana awiri a maziko ake. kutalika angapezeke mu piramidi nthawi zonse, zidziwike ngati kutalika kwa diagonals wa zapansi ndi awiri, ndi m'mphepete mwa piramidi. Tiyeni opendekera kwambiri m'munsi wofanana D1, pamene ang'onoang'ono opendekera maziko - D2, ndi m'mphepete ali kutalika - L. Kupeza kutalika kungakhale kuchokera kumwamba ziwiri zosiyana mfundo chapamwamba chithunzi m'munsi pa maziko ake. Ife tikuwona chimene ife tikuyenera Triangles awiri lamanja, mpaka kupeza kutalika kwa miyendo. Pakuti opendekera izi wamkulu wa kuchotsera aang'ono ndi kugawaniza ndi 2. Popeza mwendo umodzi ife tikupeza: a = (D1-D2) / 2. Pambuyo pake, malinga ndi Lingaliro Lovomerezeka Pythagorean, ife tikhoza kupeza mwendo chachiwiri, amene ali pamwamba pa piramidi.

Tsopano yang'anani pa nkhani zonse kuchita. Ntchito patsogolo pathu. Piramidi truncated ali apakati pa maziko a, m'munsi chachikulu cha kutalika opendekera ndi 10 cm, pamene ang'onoang'ono - 6 cm, ndi chipsyepsye ndi wofanana ndi masentimita 4 kutalika chofunika kupeza .. Kupeza chiyambi cha munthu mwendo wina = (10-6) / 2 = 2 cm wina mwendo ndi wofanana ndi masentimita 2, ndi hypotenuse - 4 cm likukhalira kuti mwendo wachiwiri kapena msinkhu adzakhala wofanana 16-4 = 12, i.e. H = .. √12 = za 3.5 cm.