Dab tsi yog qhov ncaj prism? Cov khoom thiab cov qauv. Ua haujlwm piv txwv

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2023-12-17 05:28

Stereometry yog kev kawm txog cov yam ntxwv ntawm peb-dimensional geometric duab. Ib qho zoo-paub cov duab volumetric uas tshwm nyob rau hauv cov teeb meem geometry yog ib tug ncaj prism. Cia peb xav txog hauv kab lus no nws yog dab tsi, thiab piav qhia meej txog lub prism nrog lub hauv paus peb sab.

Prism thiab nws hom

Ib lub prism yog ib daim duab uas yog tsim los ntawm ib tug sib npaug txhais lus ntawm ib tug polygon nyob rau hauv qhov chaw. Raws li qhov tshwm sim ntawm qhov kev ua haujlwm geometric no, ib daim duab yog tsim, muaj ob peb parallelograms thiab ob qho tib si polygons sib npaug rau ib leeg. Parallelograms yog ob sab ntawm lub prism, thiab polygons yog nws cov hauv paus.

Txhua lub prism muaj n + 2 sab, 3n npoo thiab 2n vertices, qhov twg n yog tus naj npawb ntawm kaum lossis ob sab ntawm lub hauv paus polygonal. Daim duab qhia txog lub pentagonal prism uas muaj 7 sab, 10 vertices thiab 15 ntug.

Cov chav kawm suav nrog cov duab yog sawv cev los ntawm ntau hom prisms. Peb sau lawv luv luv:

• oblique thiab ncaj;
• pawg thiab yog.

Txhua daim duab belongs rau ib qho ntawm peb hom kev faib tawm. Thaum daws teeb meem geometric, nws yog qhov yooj yim tshaj los ua cov lej rau cov prisms tsis tu ncua thiab ncaj. Cov tom kawg yuav tau tham ntau ntxiv hauv kab lus hauv qab no ntawm kab lus.

Dab tsi yog qhov ncaj prism?

Ib qho ncaj prism yog concave los yog convex, tsis tu ncua los yog tsis xwm yeem prism, nyob rau hauv uas txhua sab yog sawv cev los ntawm quadrilaterals nrog 90 ° kaum. Yog tias tsawg kawg yog ib qho ntawm cov plaub fab ntawm ob sab tsis yog duab plaub lossis square, ces lub prism hu ua oblique. Lwm lub ntsiab lus tseem tuaj yeem muab tau: ib qho ncaj prism yog ib daim duab ntawm ib chav kawm uas ib sab ntug sib npaug rau qhov siab. Nyob rau hauv qhov siab h ntawm lub prism, qhov kev ncua deb ntawm nws lub hauv paus yog assumed.

Ob qho tib si ntawm cov lus txhais tau hais tias nws yog prism ncaj qha yog sib npaug thiab txaus tus kheej. Nws ua raws los ntawm lawv tias txhua lub kaum sab xis ntawm ib qho ntawm lub hauv paus thiab txhua sab yog 90 °.

Nws tau hais saum toj no tias nws yooj yim rau kev ua haujlwm nrog cov duab ncaj qha thaum daws teeb meem. Qhov no yog vim qhov tseeb tias qhov siab sib phim qhov ntev ntawm sab tav. Qhov tseeb tom kawg ua kom yooj yim rau cov txheej txheem ntawm kev suav qhov ntim ntawm ib daim duab thiab thaj tsam ntawm nws sab nraud.

ntim ntawm ib qho ncaj qha prism

Volume - tus nqi muaj nyob hauv txhua daim duab spatial, uas tus lej qhia txog qhov chaw ntawm qhov chaw nyob nruab nrab ntawm qhov chaw ntawm qhov kev txiav txim siabkhoom. Qhov ntim ntawm prism tuaj yeem suav nrog siv cov qauv hauv qab no:

V=S_oh.

Yog, cov khoom ntawm qhov siab thiab thaj tsam ntawm lub hauv paus yuav muab tus nqi xav tau V. Txij li thaum lub hauv paus ntawm ib qho ncaj prism yog sib npaug, ces txiav txim siab thaj tsam S_o koj tuaj yeem nqa ib qho ntawm lawv.

Qhov kom zoo dua ntawm kev siv cov qauv saum toj no tshwj xeeb rau qhov ncaj prism hauv kev sib piv nrog nws lwm hom yog tias nws yooj yim heev los nrhiav qhov siab ntawm daim duab, vim nws coincides nrog qhov ntev ntawm sab ntug.

Side area

Nws yog qhov yooj yim los xam tsis tsuas yog lub ntim rau ib daim duab ncaj nraim ntawm chav kawm raws li kev xav, tab sis kuj yog nws sab nraud. Qhov tseeb, txhua sab ntawm nws yog ib daim duab plaub lossis square. Txhua tus tub ntxhais kawm paub yuav ua li cas xam cov cheeb tsam ntawm cov duab tiaj tus, rau qhov no nws yog ib qho tsim nyog yuav tsum tau muab faib ua ob sab ntawm ib leeg.

Xav tias lub hauv paus ntawm lub prism yog ib qho arbitrary n-gon uas nws sab sib npaug rau a_i. Index kuv khiav ntawm 1 mus rau n. Thaj tsam ntawm ib daim duab plaub yog xam li no:

S_i=a_ih.

thaj chaw ntawm sab nraud S_byog yooj yim los xam yog tias koj ntxiv tag nrho cov cheeb tsam S_i rectangles. Hauv qhov no, peb tau txais cov qauv kawg rau S _bncaj prism:

S_b=h∑_i=1(ai _)=hPo

Yog li, txhawm rau txiav txim siab thaj tsam sab nraud rau qhov ncaj prism, koj yuav tsum muab nws qhov siab los ntawm ib puag ncig ntawm ib puag ncig.

Teeb meem nrog daim duab peb sab prism

Xav tias muab lub prism ncaj nraim. Lub hauv paus yog daim duab peb sab. Ob txhais ceg ntawm daim duab peb sab yog 12 cm thiab 8 cm. Nws yog tsim nyog los xam lub ntim ntawm daim duab thiab nws tag nrho cheeb tsam yog hais tias qhov siab ntawm lub prism yog 15 cm.

Ua ntej, cia peb suav qhov ntim ntawm lub prism ncaj nraim. Daim duab peb sab (lub kaum sab xis) nyob ntawm nws lub hauv paus muaj thaj tsam:

S_o=a₁a₂/2=128/2=48cm².

Raws li koj tuaj yeem twv, a ₁ thiab ₂ yog ceg hauv qhov sib npaug no. Paub txog thaj tsam ntawm lub hauv paus thiab qhov siab (saib qhov teeb meem ntawm qhov teeb meem), koj tuaj yeem siv tus qauv rau V:

V=S_oh=4815=720cm³.

Tag nrho cheeb tsam ntawm daim duab yog tsim los ntawm ob qhov chaw: thaj chaw ntawm lub hauv paus thiab sab nraud. Cov cheeb tsam ntawm ob lub hauv paus yog:

S_2o=2S_o=482=96cm².

txhawm rau xam thaj chaw sab nraud, koj yuav tsum paub qhov ib puag ncig ntawm daim duab peb sab. Muab xam los ntawm Pythagorean theorem nws hypotenuse a₃, peb muaj:

a₃ =√(a₁²+ a₂ 2^)=√(122^{+ 8}2^{)=14.42 cm.}

Tom qab ntawd lub cheeb tsam ntawm daim duab peb sab ntawm lub hauv paus ntawm txoj cai prism yuav yog:

P=a₁+ a₂+ a₃=12 + 8 + 14, 42=34,42 cm.

Siv tus qauv rau S_b, uas tau sau nyob rau hauv nqe lus dhau los,tau:

S_b=hP=1534, 42=516, 3 cm.

Ntxiv cov cheeb tsam ntawm S_2o thiab S_b, peb tau txais tag nrho cov cheeb tsam ntawm qhov kev kawm geometric duab:

S=S_2o+ S_b=96 + 516, 3=612, 3cm^2.

Ib daim duab peb sab prism, uas yog tsim los ntawm cov iav tshwj xeeb, yog siv hauv optics los kawm txog cov khoom ntawm lub teeb-emitting. Xws li prisms muaj peev xwm decompose lub teeb rau hauv feem ntau zaus vim qhov tshwm sim ntawm dispersion.