Txhua tus menyuam kawm ntawv theem siab paub txog cov duab spatial xws li pob, lub tog raj kheej, lub khob hliav qab, pyramid thiab prism. Los ntawm tsab xov xwm no koj yuav kawm txog dab tsi daim duab peb sab prism yog dab tsi thiab cov khoom nws yog dab tsi.
Peb yuav txiav txim siab li cas hauv kab lus?
Daim duab peb sab prism yog tus neeg sawv cev yooj yim tshaj plaws ntawm cov chav kawm ntawm prisms, uas muaj tsawg dua sab, vertices thiab ntug dua li lwm cov duab zoo sib xws. Qhov prism no yog tsim los ntawm ob daim duab peb sab, uas tuaj yeem muaj qhov tsis txaus ntseeg, tab sis qhov yuav tsum tau sib npaug ntawm ib leeg thiab nyob rau hauv cov dav hlau sib luag hauv qhov chaw, thiab peb qhov parallelograms, uas tsis sib npaug rau ib leeg hauv cov ntaub ntawv dav dav. Kom meej meej, daim duab piav qhia hauv qab no.
Kuv tuaj yeem tau txais daim duab peb sab prism li cas? Nws yooj yim heev: koj yuav tsum nqa daim duab peb sab thiab hloov mus rau qee qhov vector hauv qhov chaw. Tom qab ntawd txuas qhov zoo tib yam ntsug ntawm ob daim duab peb sab nrog ntu. Yog li peb tau txais tus ncej ntawm daim duab. Yog tias peb tam sim no xav txog tias cov ncej no txwv cov sab sab, ces peb tau txaisdaim duab peb-dimensional.
Cov ntsiab lus dab tsi yog qhov prism hauv kev kawm muaj?
Ib daim duab peb sab prism yog polyhedron, uas yog, nws yog tsim los ntawm ob peb lub ntsej muag sib tshuam los yog sab. Nws tau qhia saum toj no tias nws muaj tsib sab (ob daim duab peb sab thiab peb quadrangular). Daim duab peb sab yog hu ua bases, thaum parallelograms yog sab ntsej muag.
Zoo ib yam li polyhedron, qhov kev kawm prism muaj vertices. Tsis zoo li lub pyramid, qhov vertices ntawm ib qho prism yog sib npaug. Daim duab peb sab muaj rau ntawm lawv. Tag nrho cov ntawm lawv yog nyob rau hauv ob lub hauv paus. Ob lub hauv paus ntug thiab ib sab ntug sib tshuam ntawm txhua qhov vertex.
Yog tias peb ntxiv cov lej ntawm cov lej rau tus lej ntawm sab ntawm daim duab, thiab rho tawm tus lej 2 ntawm tus nqi tshwm sim, ces peb yuav tau txais cov lus teb rau lo lus nug ntawm pes tsawg tus ntug ntawm prism raws li xav tau.. Muaj cuaj ntawm lawv: rau qhov txwv lub hauv paus, thiab qhov seem peb cais cov parallelograms ntawm ib leeg.
Shape types
Cov lus piav qhia txaus txaus ntawm daim duab peb sab prism muab rau hauv cov kab lus dhau los sib raug rau ntau hom duab. Xav txog lawv qhov kev faib tawm.
Qhov kev kawm prism tuaj yeem inclined thiab ncaj. Qhov sib txawv ntawm lawv yog nyob rau hauv hom ntawm sab ntsej muag. Nyob rau hauv ib tug ncaj prism lawv yog cov duab plaub, thiab nyob rau hauv ib tug inclined ib tug lawv yog dav parallelograms. Qhia hauv qab no yog ob lub prisms nrog peb lub hauv paus, ib qho ncaj thiab ib qho oblique.
Tsis zoo li ib qho inclined prism, ib tug ncaj prism muaj tag nrho cov dihedral kaum ntawm lub hauv paus thiabsab yog 90 °. Qhov tseeb kawg txhais li cas? Tias qhov siab ntawm daim duab peb sab prism, uas yog, qhov kev ncua deb ntawm nws lub hauv paus, nyob rau hauv ib tug ncaj daim duab yog sib npaug zos rau qhov ntev ntawm ib sab ntug. Rau ib daim duab oblique, qhov siab yog ib txwm tsawg dua qhov ntev ntawm ib qho ntawm nws sab ntug.
Prism nrog lub hauv paus daim duab peb sab tuaj yeem tsis raug thiab raug. Yog hais tias nws lub hauv paus yog daim duab peb sab nrog sib npaug sab, thiab daim duab nws tus kheej yog ncaj, ces nws yog hu ua tsis tu ncua. Lub prism tsis tu ncua muaj qhov sib luag siab, nrog rau cov dav hlau rov qab thiab cov axes ntawm kev sib hloov. Rau ib txwm prism, cov qauv rau kev xam nws cov ntim thiab qhov chaw ntawm lub ntsej muag yuav muab rau hauv qab no. Yog li, nyob rau hauv kev txiav txim.
Thaj tsam ntawm daim duab peb sab prism
Ua ntej yuav ua kom tau txais cov qauv sib xws, cia peb nthuav tawm qhov tseeb prism.
Nws yog qhov tseeb tias thaj tsam ntawm daim duab tuaj yeem suav tau los ntawm kev ntxiv peb thaj chaw ntawm cov duab plaub sib npaug thiab ob thaj chaw ntawm cov duab peb sab sib npaug nrog tib sab. Cia peb qhia qhov siab ntawm lub prism los ntawm tsab ntawv h, thiab sab ntawm nws daim duab peb sab puag - los ntawm tsab ntawv a. Ces rau thaj tsam ntawm daim duab peb sab S3 peb muaj:
S3=√3/4a2
Qhov kev qhia no tau los ntawm kev muab qhov siab ntawm daim duab peb sab los ntawm nws lub hauv paus thiab muab cov txiaj ntsig los ntawm 2.
Rau thaj tsam ntawm daim duab plaub S4peb tau txais:
S4=ah
Ntxiv cov cheeb tsam ntawm txhua sab, peb tau txais tag nrho thaj chaw ntawm daim duab:
S=2 S3+ 3S4=√3/2a2+ 3ah
Ntawm no yog thawj lo lus qhia txog thaj tsam ntawm lub hauv paus, thiab qhov thib ob yog thaj tsam ntawm sab nraud ntawm daim duab peb sab prism.
Nco ntsoov tias cov qauv no tsuas siv tau rau daim duab tsis tu ncua. Nyob rau hauv cov ntaub ntawv ntawm ib tug inclined prism tsis raug, kev xam ntawm cheeb tsam yuav tsum tau ua nyob rau hauv cov theem: thawj txiav txim seb lub cheeb tsam ntawm lub hauv paus, thiab ces - lub sab nto. Cov tom kawg yuav muab sib npaug rau cov khoom ntawm sab ntug thiab qhov ib puag ncig ntawm qhov txiav perpendicular mus rau sab ntsej muag.
ntim ntawm daim duab
Qhov ntim ntawm daim duab peb sab prism tuaj yeem suav nrog siv cov qauv sib xws rau txhua tus lej ntawm chav kawm no. Nws zoo li:
V=So h
Nyob rau hauv rooj plaub ntawm daim duab peb sab prism, cov qauv no yuav siv cov qauv hauv qab no:
V=√3/4a2 h
Yog hais tias lub prism tsis sib xws, tab sis ncaj, ces es tsis txhob ntawm thaj tsam ntawm lub hauv paus, koj yuav tsum hloov qhov sib thooj rau daim duab peb sab. Yog hais tias lub prism yog inclined, ces, nyob rau hauv tas li ntawd mus txiav txim lub cheeb tsam ntawm lub hauv paus, nws qhov siab kuj yuav tsum tau xam. Raws li txoj cai, cov qauv trigonometric yog siv rau qhov no, yog tias lub dihedral lub kaum sab xis ntawm ob sab thiab hauv paus paub.
