Mene ne diagonal na wani shigen sukari, da kuma yadda za a sami shi

Mene ne wani shigen sukari, da kuma abin da ya Diagonal

Cube (na yau da kullum polyhedron ko hexahedron) ne a uku-girma adadi, kowane fuska - shi ne mai square, wanda, kamar yadda muka sani, duk bangarorin ne daidai. shigen sukari diagonal ne a kashi cewa ya wuce ta tsakiyar adadi da kuma haɗa tsakaitã kololuwa. A dama hexahedron yana da wani diagonal 4, kuma su duka, sunã zama daidai. Yana da muhimmanci kada ya gauraye diagonal na adadi da kanta tare da diagonal fuska ko square, wanda ya ta'allaka a karkashi. Diagonal na shigen sukari ya wuce ta tsakiyar fuska kuma ya haɗu da m vertices na square.

Formula cewa iya samun diagonal na wani shigen sukari

Diagonal yau da kullum polyhedron za a iya samu a kan wani mai sauqi qwarai dabara da cewa kana so ka tuna. D = a√3, inda D wakiltar diagonal na shigen sukari, da kuma - wannan gefe. Ga wani misali daga cikin matsala, inda ya zama dole a sami wani diagonal, idan ka san cewa shi ne daidai gefen tsawon na 2 cm. Yana da sauki D = 2√3, ba ma bukatar la'akari da wani abu. A wani biyu misali, bari gefen shigen sukari ne daidai √3 cm, sa'an nan muka samu D = √3√3 = √9 = 3. Amsa: D daidai 3 cm.

Formula cewa iya samun diagonal na shigen sukari

Diago Nahl fuskoki dabam-dabam kuma za a iya samu ta hanyar dabara. Diagonals, wanda karya a fuskokin kawai 12 guda, kuma sun kasance duk daidai. Yanzu mun tuna d = a√2, inda d - ne diagonal na square, da kuma - shi ne ma wani shigen sukari baki ko gefen square. Don gane inda wannan dabara ne mai sauqi qwarai. Bayan duk, bangarorin biyu na square da diagonal nau'i mai dama-angled alwatika. Wannan uku taka rawar da wani diagonal hypotenuse da kuma gefen square - yana da kafafu da suke cikin wannan tsawon. Bari mu tuna da Pythagorean Theorem, kuma duk a lokaci daya za su fada cikin wurin. Yanzu matsalar: hexahedron baki daidai √8 gani, wajibi ne a sami wani diagonal na ta fuskoki. Saka a cikin dabara, kuma mun samu d = √8 √2 = √16 = 4. Amsa: A diagonal na shigen sukari ne 4 cm.

Idan muka sani cikin fuskõkin shigen sukari diagonal

A cewar sanarwar da matsala, ba mu kawai diagonal fuskoki na yau da kullum polyhedron, wanda shi ne daidai to, ka ce: Shin, √2 cm, kuma muna bukatar mu sami wani diagonal na wani shigen sukari. Da dabara don warware wannan matsala kadan mafi rikitarwa da suka gabata. Idan muka sani d, sa'an nan za mu iya samun gefen shigen sukari, a kan tushen da mu biyu dabara d = a√2. Muna samun = d / √2 = √2 / √2 = 1cm (wannan shi ne mu baki). Kuma idan muka sani wannan darajar, sa'an nan sami shigen sukari diagonal ne, ba wuya: D = 1√3 = √3. Wannan yadda muka warware mu aiki.

Idan sananne surface yankin

Wadannan algorithm dogara ne a kan samar da mafita diagonally a kan surface yankin na shigen sukari. Zaton cewa shi ne daidai 72 cm ^2. Don samun farkon na yankin na daya fuska, da kuma a total na 6. Sa'an nan, 72 dole ne a raba ta 6, mun samu 12 cm ^2. Wannan shi ne daya yankin da fuska. Don samun gefen akai polyhedron, shi wajibi ne don tunawa da dabara S = ^2, sa'an nan a = √S. Canza da kuma samun = √12 (shigen sukari baki). Kuma idan muka sani wannan darajar, kuma ba wuya a sami wani diagonal D = a√3 = √12 √3 = √36 = 6. Amsa: A diagonal na wani shigen sukari ne daidai da 6 cm ^2.

Idan aka sani tsawon shigen sukari gefuna

Akwai lokuta a cikin abin da matsalar da aka ba kawai da tsawon dukan gefuna da shigen sukari. Sa'an nan wajibi ne a raba ta 12. Wannan adadin na jam'iyyun a yau da kullum polyhedra. Alal misali, idan Naira Miliyan Xari da duk gefuna ne daidai da 40, daya gefen zai zama daidai da 40/12 = 3,333. Mun sanya a cikin ta farko dabara da kuma samun amsar!