Indlela yokubala umthamo wamaqumrhu ejometri eqhelekileyo

Kulo lonke ubomi bethu sihlala sibala inani leempawu okanye ezinye iimpawu zejometri. Ngoko, umzekelo, ngexesha lokwakha kuyimfuneko ukuba ubale ngokuchanekileyo umthamo weemigodi kunye neendawo. Ukongezelela, eli xabiso limiselwe phantse bonke abayili bemveliso. Xa udlula inkqubo yesikolo kwi candelo le "Geometry", uza kufunda ngokucacileyo ukuba ubale kangakanani imilinganiselo yamanani e-geometric. Kodwa kuthiwani ngabo bahlala belibale ngemisebenzi yesikolo? Eli nqaku liyakunceda ukhumbule yonke into.

Okokuqala, makhe sithethe malunga nendlela yokubala umthamo wamaqumrhu ejometri eqhelekileyo. Ezi ziquka ipiramidi, i-parallelepiped engxande, i-cone, i-cylinder, i-parallelepiped kunye ne-sphere.

Iipiramidi yiprathhedron, isiseko sayo iipoloni. Zonke ezinye iintlobo zi-triangles ezine-vertex enye. Ukuze kuqinisekiswe umthamo womzimba wejometri, kuyimfuneko ukwazi okanye ukubala indawo yesiseko nokuphakama. Umthamo wepiramidi iya kuhambelana nengxenye yesithathu yemveliso yokuphakama kunye nommandla wesiseko salolu nani. Ngendlela yohlobo, oku kuya kubonakala ngathi:

= 1/3 • S • h

Okulandelayo kwiluhlu lwethu ibhokisi. Unokubala njani umthamo walolu nani? I-parallelepiped i-prism eneparallelogram kwisiseko sayo. Ukuba bonke ubuso obune, obubizwa ngokuba bubuso bombuso, buyi-rectangles, ngoko ibhokisi ibhekiswe kumgca ochanekileyo. Ukuba onke amacala omathandathu anemirathane, ke le ngxowankulu i-parallelepiped. Umthamo waloo mfanekiso uhambelana nemveliso yamanani amabini: indawo yesiseko kunye nokuphakama komfanekiso. Ngendlela ifom, oku kungabhalwa ngokuthi:

V = S • h

Ngokuphathelele umthamo we-parallelepiped engxande, kubalwa njengomkhiqizo ubude bawo, ububanzi, nokuphakama.

= = B • h, apho

A ububanzi, b ubude, kwaye h ubude bomfanekiso.

Iqhekeza nayo ivela kwimifanekiso elula, efunyenwe ngenxa yokujikeleza kwendathathu enomnxeba ochanekileyo kwimigudu yayo. Unokubala njani umthamo weqhekeza? Kulula nje, ihambelana nesahlulo sesithathu semveliso yesiseko kunye nendawo yokuphakama.

= 1/3 • S • h

Ukongeza, umthamo wekona ungabalwa ngolu hlobo:

= 1/3 • n • r² • h, phi

N = 3.141592,

R yimizila yesangqa esisezantsi.

Ngoku khawubone indlela yokubala umthamo wesilinda? Khumbula ukuba lo mfanekiso umele ntoni. I-silinda ngumfanekiso ofunyenwe ngokujikeleza itekiti ngapha nangenye yamacala ayo. Umthamo wayo uhambelana nomkhiqizo wokuphakama kunye nomgangatho wendawo. Ifom ibhaliwe ngokuthi:

= = R² • h.

Lo mhlaba ubizwa ngokuba ngumfanekiso ovalwe, apho onke amanqaku ayo okuma asemgama omnye ukusuka kwiphakathi. Unokubala njani umthamo womzimba onjalo? Kule, kukho le fomyula elandelayo:

I = 4/3 • 3.14 • r³

Njengoko sibona ngasentla, akunzima ukubala ivolumu yimuphi umzimba wejometri, ukwazi iifomula. Ukuba ixabiso elithile kwifomula alingaziwa, kuyimfuneko ukubala, sele sele sicinge ngento efunekayo yendiza.

Ukongezelela, kufuneka kuqatshelwe ukuba zonke izithethe ezisetyenziswe kwifom eyodwa kufuneka zenziwe ngamanqana alinganayo. Umzekelo, ukuba i-radius iboniswe ngamamitha, ngoko ukuphakama kufuneka kuvezwe ngamamitha, ngaphandle koko impendulo iya kuba yinyani.

Ukongeza kwimilinganiselo yejimethri echazwe, kukho nawa manani anzima kakhulu: iipiramidi ezithiniweyo, isilinda esingenanto kunye nabanye. Kuya kubakho enye iifomula. Ngoko, umzekelo, umthamo we-cylinder engenalutho uya kulingana nomehluko kumthamo we-cylinder enkulu kunye encinci. Xa ubala le data, akukho nto inzima. Kufuneka nje ukuba umele lo mzimba kunye neqhekeza elinqunywe kuwo. Uya kubona, isisombululo seengxaki siya kuvela ngokwawo. Futhi ungaphelelwa yithemba, ukuba kukho into engasebenzi, funda nje eli nqaku ngokucophelela.