Kureba kwepiramidi. Nzira yekuiwana nayo?

Piramidi i polyhedron inobva pa polygon. Zvose zvinotarisana nezvimwe zvitatu zvitatu zvinotenderera kune rimwe vertex. Piramidhi zvinyorwa zvitatu, quadrangular uye nezvimwewo. Kuti uone kuti piramidi ipi iri mberi kwako, zvakakwana kuverenga nhamba yemakona panzvimbo yayo. Tsanangudzo ye "piramidi yakakwirira" inowanzosangana nematambudziko e geometry muchikoro chekudzidza. Muchikamu chino, ngativei kuongorora nzira dzakasiyana dzekuzviwana.

Zvikamu zve piramidi

Piramidi imwe neimwe ine zvinhu zvinotevera:

• Nechemberi inotarisana neyo mitsara mitatu uye inotenderera papepex;
• Apophema ndiko kukwirira kunoburuka kubva pamusoro wayo;
• Musoro we piramidhi ndiyo iyo inobatanidza rutivi rwomumativi, asi haararami mundiro yepasi;
• Nheyo iyi ipoloni iyo iyo vertex isinganyepi;
• Kureba kwepiramidhi chikamu chinoputira kumusoro kwepiramidi uye inoita maonero akanaka nechepamusoro.

Nzira yekuwana hurefu hwephiramidhi, kana ivhu rayo richizivikanwa

Kuburikidza nehuwandu hwemuviri wepiramidi V = (S * h) / 3 (mumutsetse V ndiro izwi, S ndiyo nzvimbo yechando, uye h ndiyo yakakwirira yepiramidi), tinoona kuti h = (3 * V) / S. Kugadzirisa nyaya, ngationei kugadzirisa dambudziko pakarepo. Mu piramidhi yerutatu, nzvimbo yebhangi iri 50 cm ² , iyo yakaita masendimita 125 cm ³ . Kureba kwepiramidi yerutatu hakuzivikanwi, uye tinoda kuiwana. Pano zvinhu zvose zviri nyore: tinonamatira dhenda yedu. Tinowana h = (3 * 125) / 50 = 7.5 cm.

Nzira yekuwana nayo urefu hwe piramidi kana urefu hwechidimbu uye mheto dzayo hunozivikanwa

Sezvatinoyeuka, kukwirira kwepiramidi kunoumba kona yakarurama nechero yayo. Uye izvi zvinoreva kuti kureba, nechepakati nehafu yekutengana pamwe chete inoumba katatu kakanyanyisa. Vakawanda, zvechokwadi, yeuka chirevo chePythagoras. Kuziva zvikamu zviviri, kukosha kwechitatu hakuzove kwakaoma kuwana. Yeuka teorem inozivikanwa e2 = b² + c², pane inonzi hypotenuse, uye kwatiri mativi emupiramidi; B - cathetus yokutanga kana hafu ye diagonal uye - pamwe chete, mutsara wechipiri, kana kukwirira kwepiramidi. Kubva pane chirevo ichi, c² = a² - b².

Iye zvino dambudziko: mune piramidhi yakarurama, iyo diagonal is 20 cm, iyo yose iyo yakareba yembambo iri masendimita 30. Zvakakosha kuwana hurefu. Gadzirisa: c = 30² - 20² = 900-400 = 500. Nokudaro c = √ 500 = inenge 22.4.

Nzira yekuwana nayo yakakwirira ye piramidi yakatukwa

Iyo ipoloni ine chikamu chakafanana nheyo yayo. Iyo yakakwirira yepiramidhi yakatenderera chikamu chinobatanidza zvigaro zvaro zviviri. Iyo yakakwirira inogona kuwanikwa mune piramidhi yakarurama kana urefu hwe diagonal hwezvigaro zvese zvirikuzivikanwa, pamwe nechepamucheto piramidi. Ngatitii iyo diagonal yekasi yepamusoro is d1, nepo diagonal yechipfuva chiduku d2, uye muganhu hurefu-l. Kuti uwane hurefu, zvinobvira kuderedza nzvimbo dzakakwirira pachigadziko chayo kubva kumativi maviri akasiyana-siyana emufananidzo. Tinoona kuti tave nemakona matatu emakona matatu, anosara kuti awane urefu hwemakumbo avo. Kuti uite izvi, kubva pane diagonal yakakura, kubvisa zviduku uye kugovana ne 2. Saka tinowana imwe yakachekwa: a = (d1-d2) / 2. Mushure meizvozvo, maererano nePythagoras 'theorem, inoramba iri kwatiri kuti tiwane gumbo rechipiri, iyo ndiyo yakakwirira ye piramidi.

Iye zvino ngationei chinhu ichi chose muchiito. Pamberi pedu pane basa. Iyo piramidi inotakura ine chikwereti muchengeti, kureba kweiyo diagonal yechipfuva chikuru ndeye 10 cm, nechecheche - 6 cm, uye nechepakati yakaenzana ne4 cm.Inotarisirwa kuwana nzvimbo yakakwirira. Chokutanga, tinowana imwe cathet: a = (10-6) / 2 = 2 cm Rimwe cathet inonzi 2 cm uye inofungidzirwa iine masentimita makumi mana (4 cm). √12 = anenge 3.5 cm.