Ke kiekie o ka pyramid. Pehea e loaʻa ia?

Pyramid - he polyhedron, i ke kumu o ka a mea he iieeaii. All maka ma ka huli palapala triangle mauna e halawai ma kekahi vertex. Nā pyramids i triangular, quadrilateral, a no laila, ma luna o. I mea e hooholo i ka pyramid i loko o ke alo o oe, ka mea, ua lawa i ka helu i ka helu o ka pana pua ma kona kumu. Ka wehewehena o "ke kiʻekiʻe o ka pyramid" ka loa, he pono ole i ka anahonua ma ka laulā maʻamau Pahuhopu. He 'atikala e ho'āʻo i ka noonoo i naʻano likeʻole o ka loaa ia ia.

pyramid māhele

Kēlā me kēia pyramid ninoieo o na kēia mau hehee wale:

• ʻaoʻao maka a i ekolu huina a converge ma ka vertex;
• apothem ho i ke kiekie, i iho mai kona luna;
• luna o ka pyramid - he wahi i hoʻohuiʻia ke kīloi paʻewa kihi, akā, i kēia 'aʻole e moe ana i loko o ka pelane o ka waihona ipu;
• kumu - he iieeaii, a aole no i ke kihi;
• kiekie o ka pyramid mea he Hoʻohana i nā keʻa i ka luna o ka pyramid a me kona kumuʻano a he huina pololei.

Pehea e loaʻa i ke kiekie o ka pyramid, ina oe i kona leo

Ma hope o haʻilula pyramid ka leo V = (S *? H) / 3 (i loko o ka haʻilula V - buke, S - wahi o ka waihona ipu, H - ke kiekie o ka pyramid), ua loaʻa i ka h = (3 * V) / S. E consolidate ka mea, e ka hoʻoponopono i ka pilikia koke. Ke triangular pyramidʻahā like ko lākou mau kumu, he 50 knm ^2, oiai kona leo, he 125 knm ^3. Unknown kiʻekiʻe o ka triangular pyramid, a me a mākou i loaʻa pono. ʻO puni hoʻi: hookomoʻikepili i loko o mākou haʻilula. E loaa? H = (3 * 125) / 50 = 7,5 knm.

Pehea e loaʻa i ke kiekie o ka pyramid, ina ua ike no kakou i ka lōʻihi o ka diagonal a me kona lua penei

E like me mākou e hoomanao, i ke kiekie o ka pyramid hana a me kona kumu akau huina. Kēia 'o ia hoʻi i ka lōʻihi o ka iwiaoao a me ka hapalua diagonally pu i hana i ka pono-huina triangle. Many, o ka papa, e hoomanao i ka Pythagorean theorem. Ike na ana elua, o ka kolu cia e e oluolu e loaʻa. Ke hoole i ike theorem a² = b² + c², a me kahi - ka hypotenuse, a ma keia hihia i ka lihi o ka pyramid; b. - ka mua wāwae a me ka hapalua diagonal a - pakahi, i ka lua o ka wāwae a me ke kiekie o ka pyramid. Mai keia haʻilula c² = a² - b².

Ano, o ka pilikia. I loko o ka diagonal akau o ka pyramid o 20 knm, oiai ka lōʻihi o ka maka - pono e loaʻa 30 knm ke kiekie .. Wehewehe i: c² = 30² - 20² = 900-400 = 500. Nolaila, = √ 500 = e pili ana i 22,4.

Pehea e imi i ke kiekie o ka truncated pyramid

He He iieeaii, a i ka pauku laua i kona kumu. Ke kiekie o ka truncated pyramid - he Hoʻohana i hoʻohuiʻia elua o kona hoʻokumuʻo. hiki ke loaʻa ke kiekie ma regular pyramid, e e ikeia ina ka lōʻihi o nā diagonals o na kumu elua, a me ke kapa o ke pyramid. E diagonal nui kumu like e d1, oiai ka uuku diagonal kahua - d2, a me ka maka i ka lōʻihi - ho'āo ai. E imi i ka mea kiekie, hiki e mai elua e ku pono ana maluna kiʻikuhi puan haʻahaʻa kiʻekiʻe ma kona kumu. Mākou iʻike i ka mea a mākou hulina loaa triangle mauna akau elua, ka mea i koe, e imi i ka loa o nā wāwae. No keia nui diagonal o ka unuhi i uuku a me ka puunaue ma 2. Mai kekahi wāwae mākou loaʻa: i = (d1-d2) / 2. Ma hope iho o ia, e like me ka Pythagorean theorem, ua hiki ke loaʻa wale nō i ka lua o ka wāwae, i mea ke kiekie o ka pyramid.

Ano, e nana i nā mea a pau i ka hihia ma ka hana. Ka hana mua mākou. Ke truncated pyramid i ka huinaha ma ka waihona ipu, ka mea i oi aku kumu o ka diagonal lōʻihi o 10 knm, oiai ka uuku - 6 knm, a me ka fin mea like i 4 knm i kiekie ua koi 'ia e loaʻa .. No ka huli ana i ka hoʻomaka o kekahi wāwae i = (10-6) / 2 = 2 knm One wāwae ua like me 2 knm, a me ka hypotenuse - 4 knm huli mai ia i ka lua o ka wāwae a kiekie, e like me 16-4 = 12, a laila m = .. √12 = ma kahi o 3.5 knm.