Lub tsev kawm ntawv cov chav kawm geometry tau muab faib ua ob ntu loj: planimetry thiab khoom geometry. Stereometry kawm cov duab spatial thiab lawv cov yam ntxwv. Hauv kab lus no, peb yuav saib seb qhov prism ncaj nraim yog dab tsi thiab muab cov qauv uas piav txog nws cov khoom xws li kab pheeb ces kaum ntev, ntim thiab thaj chaw saum npoo.
Prism yog dab tsi?
Thaum cov menyuam kawm ntawv raug nug kom lub npe lub ntsiab lus ntawm prism, lawv teb tias daim duab no yog ob qho tib si sib npaug ntawm cov polygons, ob sab uas txuas nrog parallelograms. Qhov kev txhais no yog qhov dav li qhov ua tau, txij li nws tsis txwv cov xwm txheej ntawm cov duab ntawm polygons, ntawm lawv qhov kev sib koom ua ke hauv cov dav hlau sib luag. Tsis tas li ntawd, nws txhais tau hais tias muaj kev sib txuas ntawm parallelograms, cov chav kawm uas muaj xws li ib lub square, ib lub rhombus, thiab ib daim duab plaub. Hauv qab no koj tuaj yeem pom dab tsi quadrangular prism yog.
Peb pom tias prism yog polyhedron (polyhedron) muaj n + 2sab, 2 × n vertices thiab 3 × n npoo, qhov twg n yog tus naj npawb ntawm sab (vertices) ntawm ib qho ntawm cov polygons.
Ob lub polygon feem ntau yog hu ua lub hauv paus ntawm daim duab, lwm lub ntsej muag yog ob sab ntawm lub prism.
Lub tswvyim ntawm ib tug ncaj prism
Muaj ntau hom prisms. Yog li, lawv tham txog cov duab tsis tu ncua thiab tsis xwm yeem, txog daim duab peb sab, pentagonal thiab lwm yam prisms, muaj convex thiab concave cov duab, thiab thaum kawg, lawv inclined thiab ncaj. Wb tham txog yav tas los kom ntxaws ntxiv.
A txoj cai prism yog ib daim duab ntawm cov kawm hauv chav kawm ntawm polyhedra, txhua sab quadrangles uas muaj cov kaum sab xis. Tsuas muaj ob hom ntawm cov plaub hau plaub hau - ib daim duab plaub thiab plaub fab.
Daim ntawv txiav txim siab ntawm daim duab muaj cov khoom tseem ceeb: qhov siab ntawm qhov ncaj prism yog sib npaug rau qhov ntev ntawm nws sab ntug. Nco ntsoov tias txhua sab ntug ntawm daim duab yog sib npaug rau ib leeg. Raws li rau sab ntsej muag, nyob rau hauv cov ntaub ntawv dav dav lawv tsis sib npaug rau ib leeg. Lawv qhov sib npaug yog ua tau yog tias, ntxiv rau qhov tseeb tias prism yog ncaj, nws kuj yuav raug.
Daim duab hauv qab no qhia txog tus duab ncaj nrog lub hauv paus pentagonal. Nws tuaj yeem pom tias tag nrho nws sab ntsej muag yog duab plaub.
Prism kab pheeb ces kaum thiab nws cov kab tsis sib xws
Cov yam ntxwv tseem ceeb ntawm cov prism yog nws qhov siab h thiab qhov ntev ntawm ob sab ntawm nws lub hauv paus ai, qhov twg kuv=1, …, n. Yog hais tias lub hauv paus yog ib txwm polygon, ces nws txaus kom paub qhov ntev ntawm ib sab los piav txog nws cov khoom. Paub txog cov cim linear tsis pub peb mus unambiguouslytxhais cov khoom ntawm ib daim duab raws li nws ntim lossis nto.
Cov kab pheeb ces kaum ntawm lub prism ncaj yog ntu uas txuas ob qhov tsis sib xws. Cov kab pheeb ces kaum tuaj yeem yog peb hom:
- dag hauv lub hauv paus dav hlau;
- nyob hauv cov dav hlau ntawm cov duab plaub sab;
- figures belongs rau ntim.
Qhov ntev ntawm cov kab pheeb ces kaum cuam tshuam nrog lub hauv paus yuav tsum txiav txim siab nyob ntawm hom n-gon.
Diagonals ntawm sab duab plaub yog suav nrog cov qauv hauv qab no:
d1i=√(ai2+ h2).
txhawm rau txiav txim siab ntim kab pheeb ces kaum, koj yuav tsum paub tus nqi ntawm qhov ntev ntawm qhov sib thooj hauv kab kab pheeb ces kaum thiab qhov siab. Yog hais tias ib co kab pheeb ces kaum ntawm lub hauv paus yog denoted los ntawm tsab ntawv d0i, ces lub ntim kab pheeb ces kaum d2i yog xam raws li nram no:
d2i=√(d0i2+ h2).
Piv txwv li, nyob rau hauv cov ntaub ntawv ntawm ib tug li niaj zaus quadrangular prism, qhov ntev ntawm lub ntim kab pheeb ces kaum yuav:
d2=√(2 × a2+ h2).
Nco ntsoov tias txoj cai daim duab peb sab prism tsuas muaj ib qho ntawm peb hom kab pheeb ces kaum: sab kab pheeb ces kaum.
Ntoj ntawm chav kawm ntawm cov duab
Ntog cheeb tsam yog qhov suav ntawm thaj chaw ntawm txhua lub ntsej muag ntawm daim duab. Txhawm rau pom tag nrho lub ntsej muag, koj yuav tsum ua ib qho scan ntawm prism. Ua piv txwv, xws li cheb rau daim duab pentagonal yog qhia hauv qab no.
Peb pom tias tus lej ntawm lub dav hlau yog n + 2, thiab n yog duab plaub. Txhawm rau xam cov cheeb tsam ntawm tag nrho cov cheb, ntxiv cov cheeb tsam ntawm ob lub hauv paus zoo ib yam thiab cov cheeb tsam ntawm tag nrho cov duab plaub. Tom qab ntawd cov qauv sib thooj yuav zoo li:
S=2 × So+ h × ∑i=1n (ai).
Qhov kev sib npaug no qhia tau tias thaj chaw sab nraud rau qhov kev kawm ntawm prisms yog sib npaug rau cov khoom ntawm qhov siab ntawm daim duab thiab ib puag ncig ntawm nws lub hauv paus.
Lub hauv paus cheeb tsam ntawm So tuaj yeem suav tau los ntawm kev siv cov qauv geometric tsim nyog. Piv txwv li, yog lub hauv paus ntawm txoj cai prism yog daim duab peb sab, ces peb tau:
So=a1 × a2 / 2.
Nyob qhov twg 1 and a2 yog ob txhais ceg ntawm daim duab peb sab.
Yog lub hauv paus yog n-gon nrog cov kaum sib npaug thiab sab, ces cov qauv hauv qab no yuav ncaj ncees:
So=n / 4 × ctg (pi / n) × a2.
Volume Formula
Kev txiav txim siab qhov ntim ntawm lub prism ntawm txhua yam tsis yog ib txoj haujlwm nyuaj yog tias nws lub hauv paus cheeb tsam So thiab qhov siab h paub. Muab cov txiaj ntsig no ua ke, peb tau txais qhov ntim V ntawm daim duab, uas yog:
V=So × h.
Vim lub parameter h ntawm ib tug ncaj prism yog sib npaug rau qhov ntev ntawm lub lateral ntug, tag nrho cov teeb meem ntawm kev xam cov ntim los rau xam qhov chaw So. Saum pebtwb tau hais ob peb lo lus thiab muab ob peb qauv los txiav txim So. Ntawm no peb tsuas yog nco ntsoov tias nyob rau hauv cov ntaub ntawv ntawm ib tug arbitrary-zoo li tus puag, koj yuav tsum lov nws mus rau hauv yooj yim ntu (triangles, rectangles), xam cov cheeb tsam ntawm txhua tus, thiab ces ntxiv tag nrho cov cheeb tsam kom tau S o.
