Direct daim duab peb sab prism. Cov qauv rau qhov ntim thiab qhov chaw. Kev daws teeb meem geometric

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2024-01-02 17:48

Hauv tsev kawm ntawv theem siab, tom qab kawm txog cov khoom ntawm cov duab ntawm lub dav hlau, lawv txav mus rau kev xav txog cov khoom geometric spatial xws li prisms, spheres, pyramids, cylinders thiab cones. Hauv kab lus no, peb yuav muab cov lus piav qhia ua tiav ntawm daim duab peb sab ncaj prism.

Dab tsi yog daim duab peb sab prism?

Cia peb pib tsab xov xwm nrog lub ntsiab lus ntawm daim duab, uas yuav tau tham ntxiv. Lub prism los ntawm qhov pom ntawm geometry yog ib daim duab nyob rau hauv qhov chaw tsim los ntawm ob zoo tib yam n-gons nyob rau hauv parallel dav hlau, tib lub kaum sab xis uas txuas nrog cov kab ncaj nraim. Cov ntu no hu ua lateral ribs. Ua ke nrog ob sab ntawm lub hauv paus, lawv tsim ib sab saum npoo, uas feem ntau sawv cev los ntawm parallelograms.

Ob n-gons yog lub hauv paus ntawm daim duab. Yog hais tias sab ntug yog perpendicular rau lawv, ces lawv hais txog ib tug ncaj prism. Raws li, yog tias tus naj npawb ntawm sab n ntawm polygon ntawm lub hauv paus yog peb, ces cov duab zoo li no hu ua triangular prism.

Daim duab peb sab ncaj prism yog qhia saum toj no hauv daim duab. Daim duab no tseem hu ua tsis tu ncua, vim nws cov hauv paus yog daim duab peb sab sib npaug. Qhov ntev ntawm sab ntug ntawm daim duab, qhia los ntawm tsab ntawv h hauv daim duab, hu ua nws qhov siab.

Daim duab qhia tau hais tias lub prism nrog lub hauv paus peb sab yog tsim los ntawm tsib lub ntsej muag, ob qho tib si yog daim duab peb sab sib npaug, thiab peb yog cov duab plaub zoo tib yam. Ntxiv rau lub ntsej muag, lub prism muaj rau vertices ntawm lub hauv paus thiab cuaj npoo. Cov lej ntawm cov ntsiab lus suav nrog muaj feem cuam tshuam los ntawm Euler theorem:

number of edges=tus naj npawb ntawm vertices + naj npawb ntawm sab - 2.

Thaj tsam ntawm txoj cai daim duab peb sab prism

Peb pom saum toj no tias daim duab hauv nqe lus nug yog tsim los ntawm tsib lub ntsej muag ntawm ob hom (ob daim duab peb sab, peb daim duab plaub). Tag nrho cov ntsej muag no tsim tag nrho saum npoo ntawm prism. Lawv tag nrho cheeb tsam yog thaj tsam ntawm daim duab. Hauv qab no yog daim duab peb sab prism nthuav tawm, uas tuaj yeem tau txais los ntawm thawj zaug txiav tawm ob lub hauv paus ntawm daim duab, thiab tom qab ntawd txiav raws ib ntug thiab nthuav tawm sab saum toj.

Cia muab cov qauv los txiav txim qhov chaw ntawm qhov cheb no. Cia peb pib nrog lub hauv paus ntawm txoj cai triangular prism. Txij li thaum lawv sawv cev rau daim duab peb sab, thaj tsam S_{3 ntawm lawv tuaj yeem pom raws li hauv qab no:}

S₃=1/2ah_a.

Ntawm no yog ib sab ntawm daim duab peb sab, h_{a yog qhov siab qis los ntawm lub vertex ntawm daim duab peb sab mus rau sab no.}

Yog tias daim duab peb sab sib npaug (tsis tu ncua), ces tus qauv rau S _{3nyob ntawm tsuas yog ib qho parameter a. Nws zoo li:}

S₃=√3/4a^2.

Qhov kev qhia no tuaj yeem tau txais los ntawm kev txiav txim siab ntawm daim duab peb sab yog tsim los ntawm ntu a, a/2, h_a.

thaj chaw hauv paus S_o rau daim duab ib txwm yog ob npaug ntawm tus nqi S_3:

S_o=2S₃=√3/2a^2.

Raws li thaj chaw sab nraud S_{b, nws tsis yooj yim rau xam. Ua li no, nws yog txaus los muab faib los ntawm peb cheeb tsam ntawm \u200b\u200 pob txha daim duab plaub tsim los ntawm sab a thiab h. Cov qauv sib thooj yog:}

S_b=3ah.

Yog li, thaj tsam ntawm ib txwm muaj prism nrog lub hauv paus peb sab yog pom los ntawm cov qauv hauv qab no:

S=S_o+ S_b=√3/2a^{2+ 3 ah.}

Yog hais tias lub prism yog ncaj tab sis tsis sib xws, ces xam nws cheeb tsam, koj yuav tsum cais ntxiv cov cheeb tsam ntawm cov duab plaub uas tsis sib npaug zos rau ib leeg.

Kev txiav txim siab ntim ntawm daim duab

Lub ntim ntawm lub prism yog to taub raws li qhov chaw txwv los ntawm nws sab (ntsej muag). Kev xam qhov ntim ntawm txoj cai daim duab peb sab prism yog qhov yooj yim dua li kev suav nws qhov chaw. Ua li no, nws yog txaus kom paub qhov chaw ntawm lub hauv paus thiab qhov siab ntawm daim duab. Txij li qhov siab h ntawm ib daim duab ncaj yog qhov ntev ntawm nws sab ntug, thiab yuav ua li cas xam lub hauv paus cheeb tsam, peb tau muab rau yav dhau lostaw tes, ces nws tseem yuav muab ob qhov tseem ceeb no rau ib leeg thiaj li tau txais qhov xav tau ntim. Cov mis rau nws ua:

V=S_3h.

Nco ntsoov tias cov khoom lag luam ntawm thaj tsam ntawm ib puag ncig thiab qhov siab yuav muab qhov ntim ntawm tsis yog ib qho ncaj prism, tab sis kuj yog ib daim duab oblique thiab txawm tias lub tog raj kheej.

Kev daws teeb meem

Iav daim duab peb sab prisms yog siv rau hauv optics los kawm cov spectrum ntawm electromagnetic tawg vim qhov tshwm sim ntawm dispersion. Nws paub tias lub iav prism ib txwm muaj lub hauv paus ntev ntawm 10 cm thiab ntug ntev ntawm 15 cm. Qhov chaw ntawm nws lub ntsej muag iav yog dab tsi, thiab nws ntim dab tsi?

txhawm rau txiav txim siab thaj chaw, peb yuav siv cov qauv sau hauv kab lus. Peb muaj:

S=√3/2a²+ 3ah=√3/210² + 3 1015=536.6cm^2.

Txhawm rau txiav txim siab ntim V, peb kuj siv cov qauv saum toj no:

V=S₃h=√3/4a²h=√3/410 2^{15=649.5 cm}3^.

Txawm hais tias cov npoo ntawm qhov prism yog 10 cm thiab 15 cm ntev, lub ntim ntawm daim duab tsuas yog 0.65 liters (ib lub voos xwmfab nrog ib sab ntawm 10 cm muaj qhov ntim ntawm 1 liter).